Off hand, I think few if any
non-fuel-related issues will allow an engine to be restarted.
One obscure one is of you get a single duff magneto but which is still firing, at the wrong point. This will cause a potentially extremely rough running engine, so switching to the L or R mag is worth a try.
Otherwise, assume it is fuel, so... check fuel cock is on one tank or the other, electric fuel pump on, carb heat out (on a carb engine), alternate air out (on a FI engine).
Switching tanks can be tricky, because there will be a delay before the engine restarts, which has caused some people to switch back to the original (empty) tank, after which the bit of fuel from the non-empty tank comes through, "confirming" your belief that you are on the right tank now
