This year we carried 3 qbs on the active roster bc of Alex Smith's situation. Thank goodness they carried Alex even though they probably thought he wouldnt see a snap.
Traditionally teams dont carry 3 qbs but looking at the league, seems like carrying 3 qbs is becoming more popular and the majority position.
https://www.ourlads.com/nfldepthcharts/depthchartpos/QB
^^ good easy to navigate website for roster and roster searches