I don't like to say "Impossible!" because someone can always come up with something.
It doesn't sound like a natural pattern to me right now.
In my opinion, with "offer" what should follow immediately after the verb is what you are offering.
I offered my husband's plumbing expertise. I offered to lend her my black dress.
The "to" that would come next isn't an infinitive of purpose ("to fix the leaks") but the recipient of the services.
I offered my husband's plumbing expertise to my neighbor to help her with her leaky kitchen sink.
I offered the job to the best candidate.
However, if you can think of more sentences, let's see if we can fine one in that pattern that does sound natural.