Can we use a bare infinitive after the copula freely?

But all he'd tried to do (as he shouted at Uncle Vernon through the
locked door of his cupboard) was jump behind the big trash cans
outside the kitchen doors. Harry supposed that the wind must have
caught him in mid- jump. (Harry Potter and the Sorcerer's Stone)

A great thing to do is dance the night away. (English Syntax and
Argumentation, Bas Aarts)

As long as there is a to-infinitive in the subject just like the two examples, can we use a bare infinitive after the copular? (I want to know if there are some regulations in using bare infinitives: for example, the subject has to have ‘all, what, anything, etc’)

Answer

EDIT FOLLOWING A MORE ATTENTIVE READING OF THE QUESTION
The short answer is ‘No’ A marked infinitive is obligatory, as may be seen from counter-examples:

^✲What we plan is take the train to New York.
^✲Caesar’s objective was break the power of the Druids.

The question then becomes, Why is the bare infinitive acceptable in your two examples?

I note that in these examples, the construction with a marked infinitive is equally acceptable as without:

All he’d tried to do was to jump behind the trash cans.
A great thing to do is to dance the night away.

or

All he’d tried to do was jump behind the trash cans.
A great thing to do is dance the night away.

But if we invert the predication, the marked infinitive is required:

To jump behind the trash cans was all he’d tried to do.
To dance the night away is a great thing to do.

These two facts lead me to believe that what we have here is not bare infinitives but ellipses: the marker is allowed to be dropped because in each case it is preceded by a (somewhat parallel) marked infinitive, to do. This seems to be confirmed by the fact that if we delete those to dos, the resultant unmarked infinitives are no longer acceptable:

^✲All he had tried was jump behind the trash cans.
^✲A great thing is dance the night away.