Pensieve header: Experiments with exponential zipping.

Unprotect[SeriesData];
SeriesData/:Expand[sd_SeriesData]:=MapAt[Expand,sd,3];
Protect[SeriesData];
(SuperStar[z])=ζ; (SuperStar[ζ])=z;(Subscript[Zip, {}])[P_]:=P;
(Subscript[Zip, {ζ_,ζs___}])[P_] := (Expand[P//(Subscript[Zip, {ζs}])] /. f_.(ζ^(d_.)):>(∂_({(SuperStar[ζ]),d}))f) /. (SuperStar[ζ])->0

(Subscript[Zip, {ζ}])[Series[E^Sum[(Subscript[a, p,m,n])(ϵ^p)(z^m)(ζ^n),{p,1,3},{m,0,3},{n,0,3}],{ϵ,0,3}]]