Can American football players play multiple positions? I know that in the one-platoon system, the players played both offence and defence. But in modern football can they play other positions than what they are assigned in the roster?
Absolutely they can. Many players play multiple positions. Most common is probably guys who play both Running Back and Wide Receiver(Example being Dexter McCluster - Tennesee Titans). Granted I'm guessing you're probably looking more for guys who play on offense and defense in the same game or at least the same season.
One notable guy who has played both offense and defense is Mike Vrabel who was a career linebacker, but lined up on the offensive side of the ball multiple times, with a career 14 targets in the passing game, 10 receptions, all 10 going for Touchdowns.
Multiple times have offensive linemen lined up as Full Backs or Tight Ends. JJ Watt has caught multiple touchdown passes in his short career. Now will we see a player line up on both sides of the ball on a consistent basis, game in and game out, probably not too often. It would probably lead to the player tiring out too quickly and not being as effective. But yes, a player can play multiple positions in the same game.
There is absolutely no rule against one player playing multiple positions. Most special teams players also have an offense or defense position. There are even players who play both offense and defense. A trick made famous by the Bears with William Perry is to hand the ball off to a huge defensive lineman to pick up a half yard or so.
There have even been players who played both offense and defense somewhat regularly. Deion Sanders played both cornerback and wide receiver.
While the NFL hasn't had many even occasional one-platoon players in the Super Bowl era, Arena Football was rather popular doing so. For its first 20 years [1987-2007], most players played offense and defense [it appears it was 8 on a side, only two of which were one-way players (QB+offensive specialist vs 2 defense specialists)].
The league had an Iron Man Award to celebrate the best two-way player. Found http://www.arenafootball.com/sports/a-footbl/spec-rel/062212aaf.html which lists a committee's 25 greatest of all times. Barry Wagner apparently holds both the career records for most receiving yards... and for most fumbles caused? Not bad!