One interesting crossover could be Blue Beetle seeking Batman's guidance on how to better protect his city. Batman, with his years of experience, could offer strategic advice to Blue Beetle. Another could be them teaming up against a common enemy like Ra's al Ghul. Ra's has complex plans that would require both their skills to stop.
Blue Beetle is often portrayed as a hero who is still finding his way and is full of enthusiasm. Batman, on the other hand, is a hardened veteran. Their personalities might clash when it comes to their approach to crime - fighting. Blue Beetle may want to rush in and save the day immediately, while Batman prefers careful planning. But this difference can also be a strength. Blue Beetle's eagerness can inspire Batman to be more action - oriented at times, and Batman's experience can teach Blue Beetle the value of patience and strategy.
Another idea is a time - travel fanfiction. Blue Beetle and Black Beetle could be sent back in time to a crucial moment in their predecessors' lives. They then have to make sure not to disrupt the timeline while also trying to gain some knowledge or power that can help them in their present - day battles. This would allow for exploration of their origins and how they've evolved over time.
The story where Blue Beetle teams up with other heroes like Booster Gold is really good. It shows his ability to work in a team. They have great chemistry together and face some tough challenges side by side. It's a story full of action and humor.