What happens if a 33rd team joins the NFL?

Question came up after watching a video of the history of NFL teams (pre-merger all the way to now). The 32 team setup feels pretty solid and permanent but what happens if a city was interested in starting a franchise? How would that affect division and conference alignments? Would they need to start more franchises to keep the divisions at the same number of teams?

The question is essentially, is expansion still possible in the modern era of the NFL?