Catcher injuries limit a lot of catchers from starting a ton of games, but last year no catcher started more than 123 games as a catcher. That basically means another catcher caught 25% of that team's games (or 39 games). If you split the starts up 60-40 (1 catcher catches 3 specific starters and the other 2 specific starters), the GS totals would be something like 97 to 65.
Last year, only 11 catchers started more than 98 games at catcher. Only 8 started over 105 games.
Most teams, due to injuries or whatever, already use something close to a 60-40 or 50-50 split anyways.
(On an unrelated note, fangraphs ranked the Sox second in catcher defense last year behind AZ. We were also 4th in DRS and 2nd in pitch framing.)