Alright, how about the Backside worlds?
World R7: Starry Seas
Higher up in the sky than before, islands are dotted across the water below and the stars can be seen in the deep purple sky.
Bicolor Doors variation:
Composite Doors
Combo Doors can now have multiple spend colors! A single lock must be in the region of a single spend color: for example, you can have a Combo Door with a 2 Red lock and a 1 Green lock on a White background and a 5 Blue lock on a Black background. This Combo Door will need 2 Red Keys, 1 Green Key, and 5 Blue Keys to open, and opening it spends 3 White and 5 Black.
When it comes to Glitch color, the positions of a Composite Door's spend color matter: the Composite Door's spend colors are "ordered" from left-to-right then top-to-bottom like reading, so the bottom-right-most spending color of the Composite Door becomes the new Glitch color.
I thought of two Star Key variations:
Star-Swap Keys
These Keys have a Star half on the left half of their head and an Unstar half on the right half of their head, and they swap the Star state of that Key color: if it's not starred then it becomes starred, but if it's currently starred then it becomes un-starred.
Starry Keys and Doors
These keys and doors, which can come in any color, have faint star patterns on them (behind the lock(s) in layering in the case of doors). These keys and doors take your Star state and do the opposite: they don't change your count if that Key count isn't starred, but they do change your count if that Key count is starred. Perhaps there are also "Forceful" keys and doors, which have pentagons instead of stars and will always change your count whether it's starred or not, and "Weak" doors which have X's instead of stars/pentagons and never change your count whether it's starred or not (there are no weak keys because they'd do nothing).
World R8: Cliffside Vaults
Pyramids hidden away in the Etchstone Cliffs contain fabulous treasures, but beware of those who guard the tombs!
Negative Master Key variation:
Alarm Keys
These are silver with a red and blue light on top of their head (like the lights of a police car). You can use an Alarm Key on a door to spend what that door would spend without actually opening it: for example, if you use an Alarm Key on a 4 Black Door with 3 copies, your Black count is decreased by 4 but the door still has 3 copies. You don't need to satisfy the door's requirements to use an Alarm Key on it, so this could take your Black count from 3 to -1. Doors with Alarm or Pure on them are immune to Alarm Keys (notably, Master is not immune to Alarm...).
Positive real Alarm Keys spend whatever a positive real copy of that door would spend, even if it doesn't have any positive real copies, so if you have a 4 Purple Door with -1 copies, then it appears as -4 Purple but using a positive real Alarm Key on it spends 4 Purple anyway. Negative real Alarm Keys spend what a negative real copy would spend, positive imaginary Alarm Keys spend what a positive imaginary copy would spend, and negative imaginary Alarm Keys spend what a negative imaginary copy would spend.
Like Master Keys, Alarm Keys do not work on frozen/eroded/painted doors, but they do work on cursed doors (and the curse does affect what the Alarm Keys spend).
World R9: Library Tunnels
A maze of secret passages hidden within the Lockpick Library. Books line the walls of this maze. Which path will you choose to go down?
Combo Doors variation:
Choice Combo Doors
These were already described in my previous ideas post, but I'll paste that description again here.
These are Combo Doors that have a V-symbol on them, like the formal logic symbol for OR. With these Combo Doors, you don't need to meet all of their requirements to destroy them: you only need to meet at least one, and only the locks that you do satisfy will count towards the spending. For example, if you have a Choice Purple Combo Door with a 5 Cyan lock, a 3 Green lock, and a Blast Blue lock, and you have 7 Cyans, 2 Greens, and 1 Blue, then the 5 Cyan and Blast Blue locks will count towards spending since their requirements were fulfilled, but the 3 Green lock will not count towards the spending since you don't have enough keys for it. The Combo Door will still be destroyed since you fulfilled at least one of its requirements, and a total of 6 Purple Keys (from 5 Cyan + 1 Blue) will be spent.
It's possible to nest the two Combo Door types into a single Combo Door: for example, you could have a regular Combo Door where one of the locks is a 3 Red Lock while the other "lock" itself consists of a choice between a 4 Pink Lock and a Blank Black Lock. If a Combo Door has "layers" like this, then those layers will always alternate between regular and choice (because otherwise things that could go on the same layer would be put on different layers), and the outlines that separate the layers will be given alternating colors, where one color is the spend color and the other is a slightly tinted version of the spend color; since the inner layers don't have their own spending colors, only the outermost "locks" can be in different spending colors if the Combo Door is Composite. To make things clearer, if a Combo Door is layered like this, then the layers that are Choice Combo Door will have a V symbol on them and the layers that are regular Combo Door (i.e. where every requirement on that layer must be met) will have an upside-down V symbol on them (the logical symbol for AND).
World R10: Outdated Nexus
An older, outdated model of the Mechanical Nexus. Most of its machines have ceased to whirr, and the lights have mostly gone off. The few machines still active are slowly lagging behind their quotas.
Glitch Keys variation:
Laggy Glitch Keys
This world introduces darker Glitch Keys and Doors known as "laggy" Glitch. The first time the Glitch color is changed, the Laggy Glitch mimic doesn't update, and afterwards it lags behind the regular Glitch color by one: for example, if you open a Pink Door, then a Cyan Door, then the regular Glitch color will be Cyan but the laggy Glitch color will be Pink. If you then open a Purple door, the Glitch color changes to Purple and the laggy Glitch color changes to Cyan. Of course, if you open multiple doors of the same color in a row, then the two Glitch colors will agree, since one door ago and two doors ago are the same color. Laggy Glitch is not a separate color, so if collected on its own, it counts as Glitch, and its mimic will start as Glitch and stay that way after the first door you open, then start changing after the second door you open. Laggy Glitch has the same interactions with Brown as regular Glitch does. Purity Gates with Glitch on them prevent all Glitch color changes: for the purposes of Glitch colors, doors opened while touching a Purity Gate with Glitch on it are skipped in the Glitch color order. Composite Doors trigger multiple Glitch color changes right in a row, so the last spend color of the Composite Door becomes the new Glitch color, the second-to-last spend color of the Composite Door becomes the new Laggy Glitch color. Later in the world, even laggier Glitch Keys are introduced: Double-Lag Glitch Keys (dark green border) are two colors behind, Triple-Lag Glitch Keys (dark red border) are three colors behind, Quadruple-Lag Glitch Keys (dark blue border) are four colors behind, and so on (with different dark-colored borders).
(EDIT, because I forgot these) Lockless Door variation:
Colorless Doors
These doors have locks, but no Spend color. This is probably indicated by the door's exterior being a transparent black, but its locks are not transparent. When a Colorless Door is opened, it doesn't spend any of your Keys. The Glitch color(s) cannot be Colorless, so when a Colorless Door is opened, the Glitch color does not update. (Alternatively, perhaps the Glitch color(s) can be Colorless, but when you pick up a Colorless Glitch Key, no Keys are gained)
World R11: Miracle Chasm
The Miracle Tower overlooks a great chasm at the edge of the world, splitting the world as we know it from the complexities that lie in the Great Beyond. From the balconies of the tower, streams of light can be seen pouring up from the chasm.
Yeah, yeah, I know the quaternions are usually the next step after the complex numbers, but in my opinion, the quaternions would be more trouble than they're worth in I Wanna Lockpick. All three non-real quaternion units square to -1 (so there isn't much gameplay richness added that the complex numbers didn't already have), and the non-commutativity of multiplication would probably make the puzzle logic just too complicated to follow. Instead, I've chosen something more intuitive but also, at least in my opinion, more interesting.
Complex numbers variation:
Split-Complex Numbers
The split-complex numbers are similar to the complex numbers, but instead of the imaginary unit i where i^2 = -1, they have the "hyperbolic unit" j, where j^2 = 1. This world throws these split-complex numbers into the mix, including Split-Swap Keys (×j), Signflip Split-Swap Keys (×-j), Keys and Locks with multiples of j as their costs, and another eyepiece for the Lens of Truth that adds J-View so you can make and view split-complex copies of doors. Split-complex numbers are arguably more intuitive gameplay-wise than regular complex numbers: since j^2 = 1, Split-Swap Keys just swap your real and split-complex counts without throwing on extra negative signs. This means that positives and negatives are more separate than they are with regular complex numbers, which allows for different puzzle designs.
Regular complex numbers still exist, though, so what happens when Rotor and Split-Swap Keys show up in the same puzzle? The system that combines the complex and split-complex numbers is called the tessarines, and it introduces a fourth unit, which I'll call h instead of k to make it clear that these aren't quaternions: i * j = h, j * h = j * (i * j) = i * j^2 = i, i * h = i * (i * j) = i^2 * j = -j, and h^2 = i^2 * j^2 = -1. Rotor Split-Swap Keys (×h) and Signflip Rotor Split-Swap Keys (×-h) exist, keys and locks can use h just as well as the other three dimensions, and that additional Lens of Truth piece also added H-View. Despite this being a four-dimensional system, multiplication is still commutative.
Yes, h could just be called "ij", but that would be confusing in gameplay because you'd see a door that needs 2ij Black Keys and would probably be confused - naming ij "h" makes it clear that it's a separate unit, even if you often get there by multiplying i and j.
The various things that are separate for real and imaginary (Blast Doors, Master Key types and Lens views, imaginary Checkerboard Keys, Duality Keys, etc.) are also separate for j and h. j Blast Doors are represented via an X with a hole in the middle (so the four diagonal lines are separated), and h Blast Doors are represented via a + with a hole in the middle.
(EDIT, because I forgot these) All Doors variation:
Magnitude Doors
Whereas positive doors have dark locks and negative doors have light locks, magnitude doors have grayish locks. Magnitude doors care about the absolute value of your Key count in that dimension, but not its sign, and they'll spend in whatever sign you do have: for example, a Magnitude 3 Blue lock will spend 3 if you have 3 or more Blue Keys, it'll spend -3 if you have -3 or less Blue Keys, and it won't open if your real Blue Key count's absolute value isn't at least 3. Magnitude doors still only care about their own dimension, so real and imaginary (and split and tessarine) are still separate.
Negative copies of magnitude locks are the same as the original, though imaginary copies are different. An Exact 4 Magnitude lock needs your Key count of that color to be 4 or -4, but is fine with either of those two.
What really makes this an All Door variant is that Blast locks can also be Magnitude, so a Magnitude real Blast Door spends all your real Keys of that color regardless of sign (as long as you don't have exactly 0 of them) but doesn't consider or touch your imaginary Keys - sort of the halfway point between a regular Blast Door and an All Door. A Magnitude All Door would just be an All Door again.