There are many ways to allow two styles at once
Pummeling style specifies unarmed attacks only
Ascetic style lets you treat a weapon's attacks as unarmed strikes
both of these are specific cases, so the specific over general rule doesn't apply.
If one has ascetic style and pummeling style active their weapon attacks are treated as unarmed strikes and their unarmed strike damage from a full attack is totaled before applying DR.
Can one employing both of these feats add up their weapon damage before applying DR?
I'm sure this has been answered officially before but I can't find it.
Benefit: Whenever you use a full-attack action or flurry of blows to make multiple attacks against a single opponent with unarmed strikes, total the damage from all hits before applying damage reduction. This ability works only with unarmed strikes, .
As Ascetic Style has no "this works even with things that say they don't work with anything" language, they don't work together.