Why?
You can be a paladin (vengeance) of Thor, a cleric (trickery) of Loki, and a warlock (chain - fey) with a pact to the Svartalfar (dark elves).
There are no limits, rejoice in that, and come up with cool and intriguing character concepts.
I said I could see issues, not necessarily insurmountable ones, but issues. YMMV but for me the pact beings, especially the Arch Fiend and the Great Old One, ARE deities for all intents and purposes - especially to themselves. The Fey maybe somewhat different, but still would have the arrogance of a god...they're back door deities, really.
That being the case, I'd imagine they might get the hump (or tentacle) were their chosen one to start worshipping "another" god. Some have enough parallels to work, but in your example above I don't think Thor would share time with the dark elves. Loki, sure. But then, it's about what the secondary deity thinks too..."yes I will grant you my boon and allow you to channel my divine power...hang on, mate, you're gonna have to stop hanging out with cthulthu. That's not in the deal."
MC rogue, wizard, fighter, barbarian, Druid (for fey maybe), ranger, bard, even Sorceror (it's not their fault they're a conduit for power, nor surprising really with their background as a devotee of a powerful cosmic being - "it...it just started pouring out of me...why am I blue?").
I think there my be interesting RP scenarios that could come out of MC divine follower classes but they'd involve a certain struggle to pull off.
Me, I think the whole Pact aspect is what makes multi classing with a secondary divine entity difficult to square - from both the warlock's being and the new god. But hey, each to their own.