Trading Out Detain for "Suppress"

Detain doesn't seem to be fitting well, though I do need a mechanic in U/W that matches the controlling/defensive/reactive playstyle I want for them.

Blue and white both have the ability to alter and set a creature's base power and toughness. What if I gave them a mechanic that essentially temporarily represses power and toughness boosts?

So the big question here is what it means rules-wise that a creature loses all modifiers. What I have in mind is anything from instant effects, enchantments, equipment, and even counters that alter a creature's base power and toughness. But what does that do to */* creatures? Typically when U/W meddles with a creatures abilities or removes their abilities the ability gives the creature a base power and toughness to avoid a situation where a creature has an undefined power or toughness. Does this effect abilities that set a base power and toughness on a creature?