As noted, the North may have only wanted new states if they were likely to produce pro-Union (generally Republican) votes.
However, Congress put a lot of different rules in place for what different states had to do to be readmitted to the Union. If Congress/President pushed for a slightly different (possibly harsher) reconstruction, they could produced some "balkanization" in the process, either:
1) Mandating some splits. For example, Texas had previously (when originally admitted to the Union) had to give up a lot of claimed land in exchange for debt relief. Congress could have said, "You've incurred more debt here, so you need to give up this specified land." That could either go to neighboring (non-CSA) states or become a new state.
2) Imposing harsh requirements for readmission but allowing portions of states to "secede" to avoid them. For instance, they could make it hard for a plantation state to rejoin, but allow citizens of areas that didn't apply to to form their own state that could easily rejoin. The remainder of the state would then have to accept the split to rejoin.
During the Civil War, Virginia was partitioned into two states. There were plans like this for East Tennessee, North Georgia, and the Rio Grande. How much could the Union split up Southern states, and how would this effect post-war politics?