Bildung des past perfect mit Modalverben = Konditional II
Modalverb +have + Partizip II
could have gone könnte gegangen sein
might have done könnte möglicherweise gemacht haben
should have written sollte geschrieben haben
needed to have read sollte gelesen haben (müsste gelesen haben)

Folglich kann mit dem simple past der entsprechenden Modalverben kein past perfect gebildet werden, wir müssen wieder, wie schon beim present perfect, auf eine Umschreibung ausweichen.

Beispiele
Hilfsverb Umschreibung Umschreibung im past perfect
can => to be able to had been able to
may => to be allowed to had been allowed to
must => to have to had had to
to be obliged to had been obliged to
to be forced to had been forced to
to be compelled to had been compelled to
shall => to be to had been to
will => to want to had wanted to
to wish had wished to