There can be any amount of quarterbacks on a team at any given time. The required amount of quarterbacks on a roster to start a game is two, one starting quarterback and a backup quarterback. Most teams like to keep three quarterbacks on the roster during the season in case of injury. There can be any number of quarterbacks on the field at once, so long as there is only one playing the quarterback position (meaning there can be one quarterback at the quarterback position, while another quarterback can be on the field playing the running back position). This is a very unorthodox strategy and is rarely used.
Like any other sport, having multiple players that play the same position is highly recommended- especially for an important position like the quarterback. This way, coaches have backup players in case of any injury. Quarterbacks need to be kept injury-free and avoid any blitz collisions with defenders. It's not possible for a team to carry on without one, so quite a few can train at once and go in when they are needed.
Some collegiate level teams also employ two or three quarterbacks on the field at once, but only one is in the actual quarterback role. This is a rare strategy, but it could help a team offensively. With multiple players who are familiar with where to look for passes, utilizing a quarterback in other receiving positions can raise a team's chances of finding open lanes and landing passes. However, this is rare, because many quarterbacks are only used in their quarterback position and then kept off the field to avoid any unnecessary injury.