(finally got some time to explain further)
Let's use Shula and Frost for this example. Currently Frost is a little on the old side for a Digimon partner, but that's fine. During their various adventures that little BlackAgumon learns to Digivolve into DarkTyrannomon. Based then on Shula's influence and the needs of a specific task, Shula could push his evolution in different directions. BlackAgumon doesn't have many varying evolutions - they're mostly big dinosaur-like things: BlackGreymon, BlackGrowlmon, DarkTyrannomon) but maybe their current task requires wings. Because of Shula's power, perhaps frost is able to evolve into ExVeemon (Black) - or some other winged Champion. At the Ultimate Level - MetalTyrannomon - maybe there's a task that requires a different set of armaments/equipment/abilities than what MetalTyrannomon is able to bring to the table. So Shula is able to push Frost into a slide evolution - maybe something like BlackWarGrowlmon, Gigadramon, MasterTyrannomon. The only thing unaffected by this power is their mega form, a result of Biomerge Evolution which requires the Tamer's full power.
For Shula and Frost it's pretty limited. Like I said, BlackAgumon isn't that diverse.
But let's say the partner Digimon was something like...Gatomon. In addition to varying slide evolutions to...D'Arcmon (or whatever), it could also Armor Evolve - so long as "Shula" had the accompanying Digimental - to forms that would suit specific purposes and needs (underwater, flying, close combat, etc).