Crossovers in the 'Harry Potter' fandom really depend on what kind of mixing you're hungry for. The major archives aren't built for them, so it's a hunt. FanFiction.net's crossover category is a total mess, but it's massive. You have to filter by fandom and then sort by favorites or reviews; otherwise, you're wading through a decade of abandoned WIPs and crackfic. I found a shockingly good 'Harry Potter'/'The Dresden Files' fusion there years ago by searching the crossover section for both fandoms. AO3 is better for niche pairings across worlds, like Harry ending up in Middle-earth. The tagging system saves you, but you have to know how to use it—search for "Harry Potter" and then filter to include the second fandom, or use the "Crossover" tag.
Don't sleep on spacebattles or sufficientvelocity forums either. That's where you find the weird, crunchy, plot-heavy stuff, like a rationalist Harry thrown into the 'Worm' universe or a magical theory deep-dive crossover with 'A Song of Ice and Fire'. The prose isn't always polished, but the ideas are wild. I'd actually recommend starting with a rec list on a fandom blog or a TV Tropes page to find the classics—'Browncoat, Green Eyes' (Firefly crossover) or 'The Havoc Side of the Force' (Star Wars crossover) are pillars for a reason. It gives you a quality filter before you dive into the archive slush pile.