Is there no way to wrap up more than 2 limbs or am I just bad at the game?
There is. In the last phase you have to let go and then pick a different combination of limbs. Then a 3rd grabbing tentacle should unlock, and when you used that one then a 4th.
Yes, I admit that this progression step is a bit unintuitive. Maybe I should change it so that after the player performed the first penetration I don't unlock the second penetration tentacle but the 3rd grabbing tentacle, and only when the girl is suspended I start unlocking more penetration tentacles.