New Kitten / Resident Cats' Litter Box

Okay, so Lizzy and Sophie (more so Sophie) is accepting Luka (kitten) reluctantly.  I still have him overnight in his foster room with his own litter box and theirs is not being used by him.  I'm hesitant to let him use their box because I'm so worried Lizzy will get territorial again and start spraying.  When do I know when is the right time to let them all use the litter boxes together in the litter room?  I think I'm gonna add a couple more boxes for safety!!!

Any advice appreciated!!

My multitude of own and fosters have down well with at least 3 rooms in different corners of a home having 1-2 litterboxes each. Limits the fear/bullying near/in boxes, keeps cleaner, allows privacy, so we don't have a bout of cystitis or obstruction. For 3 cats I'd have a litterbox in 3 rooms plus the iso/foster room's litterbox.

Cleaning daily helps bigtime with box avoidance too!

Thank you!  I'm gonna get more litter and a couple more boxes.  I'm running out of rooms tho!