There are currently about 11 catchers in extended spring (based on the roster Jim Peyton posted at phuturephillies recently). Two of them are 2018 international signees (Nava and Wang), so between the two groups there are 16 catchers. There are three other guys who are still on short-season stateside rosters, but who are not listed as in XST (Nerluis Martinez, Jesse Wilkening, Juan Mendez), and three additional catchers listed on DSL rosters. A big crowd.
Some of these guys will not be on active rosters when the short season and DSL clubs begin play - some may be held in the Dominican Academy, and some will likely be released.
However, there are five rosters here - Williamsport, GCL East, GCL West, DSL Red, DSL White. These rosters have 35-player active limits, so the Phils could easily assign three catchers to each roster.