Not without presenting probable cause that the surveillance would produce evidence of a crime to a judge it can't.

Of course it can (and is well documented to have, on many occasions) just ignore the statutory and Constitutional restrictions on domestic surveillance. And that will probably, in most cases, be easier than going to a third party. Information sharing is most likely to be efficient when the other agency had a targeted surveillance operation already in place covering a target of interest, rather than in the naive “on demand” form.