I suppose I'm trying to get too granular which is leading to more work than necessary. My hope was that grant alter could be broken down into more specific permissions rather than giving the ability to all things it allows.
You mentioned schema ownership which leads me to another question. Suppose I have the three schemas: Schema1, Schema2, and Schema3. If all three are owned by dbo and a database role, Role1, has alter permission on the dbo schema, then will that also give them alter on Schema1-3? What if Schema3 is owned by database role, Role3? Would Role1 then only have alter on Schema1 and 2 since Schema3 is now owned by Role3? Conversely, would Role3 only have alter on Schema3?