One idea could be that the Scooby Gang from Buffy teams up with the BAU from Criminal Minds to solve a series of murders that seem to have a supernatural and a psychological aspect. Maybe the murders are being committed by a demon that is using human psychological weaknesses to target its victims.
Another interesting concept is that a character from Criminal Minds somehow gets transported to the Buffy universe. They have to adapt to the existence of vampires, witches, and demons while also using their profiling skills to figure out a mystery that's plaguing Sunnydale. For example, they could be trying to find out who is behind a new type of vampire behavior that seems more organized than usual.
Maybe in the fanfiction, a member of the CSI team has a personal connection to a case that the Criminal Minds team is investigating. This could lead to some intense emotional moments and also some friction between the two teams as they try to balance the need for objectivity with the personal investment. The story could explore how they overcome these challenges and solve the mystery behind the crimes.
One interesting plot idea could be a serial killer who targets both the FBI agents from Criminal Minds and the SWAT team members. The two teams have to combine their skills, with the Criminal Minds team analyzing the killer's psyche and the SWAT team providing on - ground protection and tactical support. For example, the killer might be leaving cryptic messages that only the profilers can decipher, while the SWAT team has to deal with the physical threats the killer poses during their investigations.
One idea could be that the Scorpion team is called in to help the Criminal Minds team with a case involving a highly intelligent criminal who is using complex technology to carry out their crimes. For example, the Scorpion team could use their skills to decrypt the criminal's encrypted messages that the Criminal Minds team couldn't crack on their own.
There could be a fanfiction where the Teen Wolf gang travels to a city where the Criminal Minds team is based. They notice some odd killings that seem to be related to a supernatural force. The BAU starts to investigate, not realizing the true nature of what they're dealing with at first. As the two groups interact, there are misunderstandings, like when the BAU tries to profile Scott as a potential suspect because of his enhanced abilities. But eventually, they join forces. Scott shares his knowledge of the supernatural world with the BAU, and the BAU uses their profiling skills to track down the real culprit, which is a powerful supernatural being that has been using human proxies to carry out its killings.
One idea could be that the BAU team from Criminal Minds is called in to investigate a series of murders that seem to have a connection to Dexter's 'hobby'. Dexter, being the secret serial killer who targets other killers, might initially be a suspect. Then, as the story unfolds, they could end up working together to take down a bigger network of criminals that neither could handle alone.
Well, a cool plot might be that Sherlock and Reid from Criminal Minds get into a battle of wits over a case. The case could involve a super - intelligent criminal who is playing mind games with both of them. Or perhaps there's a case where the BAU's profiling skills are needed to understand the motives of a criminal that Sherlock has been chasing, but can't quite figure out the 'why' behind the crimes. And they end up learning from each other's methods.
One idea could be that the BAU team is called in to investigate a series of strange disappearances that seem to be related to a haunted location that Teamiplier has explored in one of their videos. The two groups initially clash due to their different approaches, but then they start to work together and combine their skills to solve the mystery.
A crossover with 'Sherlock' would be cool. Imagine Sherlock's deductive reasoning combined with the BAU's psychological profiling. They could be working on a case that involves a criminal mastermind who is playing mind games with both teams. Sherlock might initially be dismissive of the BAU's methods but then come to respect them as the case progresses.
One idea could be that the BAU is called in to help the NCIS LA team when a series of murders seem to be related to a military - civilian connection. The agents from both teams could clash at first due to different working styles, but then gradually learn from each other and solve the case together.
Perhaps a fanfiction where a member of the Criminal Minds team, say Reid, gets framed for a crime that involves national security, which brings in the NCIS. The NCIS team initially suspects Reid but as they dig deeper, they realize he's been set up. Together, they work to clear Reid's name and find the real perpetrator who is using the situation to cover up a much larger conspiracy that spans both military and civilian sectors.