Consider the below sentences.
We do not have much time in which to do it.
There is the item with which to do the task.
I think these constructions are called infinitival relative clauses, a combination of infinitival clauses and relative clauses. In infinitival clauses, it is possible to introduce a subject by means of 'for': This is a task for you to do, etc.
Is it possible to do the same in these constructions? In other words, is the sentence There's not much time in which for you to do it grammatical. If not, why not?