Nope on Celtic - 8 games.
Levadia Tallinn is an interesting one. I have six games for them, four for FCI Levadia Tallinn, and two for Levadia Maardu. Wiki suggests they might actually be all the same club though. In which case that's our new leader with 12 games
So good call on that. But still leaves us looking for the other club that's played LoI sides 10 times.