Not UEFA rules, no.
I really do think there are some rules regarding loans.
Ive yet to see a club have LOADS of loans at any 1 time, unless my memory is bad?
That is why im searching for it. The only certainities i think we can be concrete with are;
2 domestic loans, 4 across a season but only 2 at any one point.
No two players from one other premier league club.
The rest of it seems very open to a club stock piling loan players, but I cannot yet find any definitive number other than this 8, to 7, to 6 rule, which does state both IN and OUT. which suggests 6 maximum loan players.
As you say, never once seen a premier leageu side with that many loans.
If we want to go by Football Manager rules, EFL clubs have a maximum of 5 long-term loans per season. You would think there would be a similar limit for EPL clubs.