As I see it if someone from state A shoots someone form state B inside of state C he could be tried by all three states, plus the federal government. for a total of four times.
States generally don't make it a crime to kill one of their residents outside that state, or make it a crime for one of their residents to kill someone outside of that state. In your scenario, this would be a crime in state C and maybe a federal crime (the federal government would need some justification to get involved; maybe the victim is a federal employee) but not a crime in state A or B.
If you exploded a bomb at a state line, I suppose you could commit murders in multiple states with a single act. However, the murder of Jane in Kentucky and Joe in Tennessee would not really be a "single crime"; that's two crimes (and it would be two crimes even if it didn't cross state lines.)
If you had a convoluted enough conspiracy to commit murder (you hire the best chemist from all 50 states to make the deadliest poison they can, then mix them together and feed it to your victim) it would be possible for you to be charged in all 50 states, plus the federal government. However, this would require that an act to further the conspiracy be performed in each state. So it's arguable whether this counts as a "single crime".
If the person somehow had a restraining order filed against him in all 50 states plus federal court, he could be tried in each state for violating the court orders with a single act. Again, it's arguable whether that counts as a "single crime".
It's worth noting that territories such as Guam, Puerto Rico, or Washington DC count as being under federal jurisdiction already - you cannot be tried under DC law and then again under federal law for the same crime. See Grafton v. United States, 206 U.S. 333 (1907). And in Waller v. Florida, 397 U.S. 387 (1970), it was ruled that cities count as political subdivisions of the state, so you cannot be tried by the state and again by a city in the state.
However, in United States v. Wheeler, 435 U.S. 313 (1978), the Supreme Court ruled that Indian tribes can have their own sovereignty, and it is not a violation of double jeopardy to be tried and convicted under tribal law and again under federal law. So, instead of the maximum number of trials in some convoluted scenario being 51 (50 states plus federal), you'd also have to add all tribes that still have sovereignty.
Are there any other situations/ways that could lead to a larger number of trials for any one crime?
Just have the jury keep hanging. I don't think there's any limit to how many times a trial that ends in a hung jury mistrial can be retried.
He could also be sued for damages in civil court, possible in all three states? so as many as 7 times if you count civil court as being 'tried'.
Why are you being sued in 3 states? Are there 3 people who were separately harmed by your actions? If so, there's no requirement that those people need to be from different states - each can file their own action regardless. If you harm a million people, a million people can file a lawsuit against you. But if one person is trying to sue you in 3 different jurisdictions, the courts aren't going to allow that.