Hello! Hm... I will say yes because I think I allowed this for Prejoin games as well.

Idol Factory cards, once you unlock them, work like member singles where you get unlimited copies of it! However, you can only trade type for type so say you unlock your 6th member (which would be the 06 card) then you can only trade it for another player's 6th member card.

I hope this helps? ^^