How do I start convincing Anna to invite people in the studio? Really want a threesome with Charlotte, is that even an option?
In order to convince Anna to invite people in the Studio, you have to choose the Slut Route first. After that, progress with the Main Storyline until Anna has 4 or 5 Hearts and make sure you already completed her Inner Regret Questline.
As for your question about Charlotte, make sure you went to Charlotte's Yacht first and when you're given 2 dialogues indicating Charlotte's or Anna's Route, pick Anna's. Then continue visiting Charlotte until you're having a threesome with Charlotte and Anna on the Yacht. Only by then you can invite Charlotte to the Studio.