Option saying which heads a structural operation may descend through — All allows any non-atomic head
AllowedHeads
Total[f[f[1], g[2π]], ∞, AllowedHeads -> {f, g}]
→ Total[f[f[1], g[2*Pi]], Infinity, AllowedHeads -> {f, g}]Total[f[f[1], g[2π]], ∞, AllowedHeads -> Inherited]
→ 3 + PiTotal[f[1, g[2π]], ∞, AllowedHeads -> All]
→ 3 + Pi