can some one use a polynomial one-to-many reduction for NP-comp problems?
I think what you are looking for is the notion of polynomial-time Turing reduction, denoted $\leq_{T}^{p}$ (also called Cook reduction, since this was the notion of reduction Cook used in the paper in which he defined NP-completeness; poly-time many-one reductions are called "Karp" or "Karp-Levin" for a similar reason), or polynomial-time truth-table reductions, denoted $\leq_{tt}^{p}$.

For any notion of reduction, you get a notion of NP-completeness: e.g. a problem is "NP-complete under $\leq_{T}^{p}$ reductions" if it is in NP and every problem in NP $\leq_{T}^{p}$-reduces to it.  The different notions of completeness are a priori distinct; however, even if they are distinct, showing that a problem is NP-complete under Cook reductions is still good evidence of its intractability.

Terminologically, when people say "NP-complete" without further specifying, they usually mean NP-complete under many-one reductions.

Lutz and Mayordomo showed that if NP does not have measure 0 in EXP,  there are problems that are NP-complete under $\leq_{T}^{p}$-reductions that are not NP-complete under $\leq_{m}^{p}$-reductions. The Lutz and Mayordomo paper has lots of other references, but one result that should be mentioned is that (under no assumptions), there are problems that are  $\leq_{T}^{p}$-complete for $NE$ that are not $\leq_{m}^{p}$-complete for $NE$ [1,2].

Truth-table reductions can be viewed either as a multi-query version of many-one reductions (in a sense they are "many-many") or as non-adaptive Turing reductions, or as Turing reductions in which all the queries are made in parallel.  The idea is that the reducing machine looks at the input, decides all the queries it's going to make without asking any of them, then asks all of them and gets answers from the oracle, then decides its answer without making further queries.

[1] H. Buhrman, S. Homer and L. Torenvliet, Completeness for nondeterministic complexity classes, Math. Systems Theory 24 (1991) 179-200.

[2] O. Watanabe, On the Structure of Intractable Complexity Classes, PhD thesis, Tokyo Institute of Technology, 1987.