Crossover method is easy. Bob established that every universe is out there somewhere in the never-never, just really far away. Even Spider-Man.
So Harry can get anywhere, and it can be via mistake using his mom's amulet and ruby.
As for what series, I'd like to see him with Doctor Who. His murphyonic field messing with the TARDIS and sonic screwdriver, Who breaking the law against time travel, Molly there flirting with the doctor only to realize she's found the only other man in existence that will never actually be with her... Lots of potential for hijinks.