ExcudedForms for Simplify

We shall define

Simplify2[e_, opts__]

admitting an option

ExcludedForms

, just like

FullSimplify

does.

The idea behind, is to wrap parts matching excluded patterns around with

Hold

, do the simplification and restore held parts back to normal.

In[38]:=
Options[Simplify2] =
  Union[Options[Simplify], {ExcludedForms :> {}}];

In[39]:=
Simplify2[e_, (opts___)?OptionQ] :=
Catch[Module[{popts, tag, ef, p},
 popts = FilterOptions[Simplify, opts];
 ef = ExcludedForms/.{opts}/.Options[Simplify2];
 If[ef === {}, Throw[Simplify[e, popts]]];
 ef = Alternatives @@ ef;
 Simplify[
    e /. RuleDelayed @@ {p:ef, Hold[tag[p]]}
 , popts] /. {Hold[tag[p_]] :> p}
]]

In[40]:=
Simplify2[Sin[x]^4 + Cos[x]^4 + Sin[x]^2 + Cos[x]^2]

Out[40]=
(1/4)*(7 + Cos[4*x])

In[41]:=
Simplify2[Sin[x]^4 + Cos[x]^4 + Sin[x]^2 + Cos[x]^2,
  ExcludedForms -> {(_Sin | _Cos)^4}]

Out[41]=
1 + Cos[x]^4 + Sin[x]^4

Enjoy!