It depends on how you define rings.
If you want rings like Saturn's, then unfortunately no, those beautiful wide and bright rings are held in place by its own gravity and the gravity of its various moons, all of which rotate around basically the same axis. Any additional rings would need other moons orbit on a different axis to generate and sustain them.
As for different axis... it gets very very complicated very quickly, i'd recommend looking at the Astronomy.SE question Could a cross-ringed planet exist for more information.
Very narrow rings on different axis are possible but short lived, all you have to do is look at the amount of debris orbiting earth to see that a fair amount of it orbits in vastly different axes. But it would take tens of thousands of years for those debris fields to form rings, very narrow ones at that, and by then they would likely have de-orbited and burnt up in the atmosphere. But for a short time it would have formed a couple of very thin rings.