How unique are the MSW parameters ?

We investigate the effect of a possible large frozen-in magnetic field in the core of the sun and a neutrino magnetic moment of the order of $10^{-10}$ Bohr magneton on the MSW parameters. Such a possibility can completely depolarize the $\nu_{eL}$ resulting in a factor of half of the emitted number. This in combination with MSW can explain the present experimental data on solar neutrinos but with a different region of the parameter space than the regular MSW alone. In this scenario there is a larger region of parameter space allowed. There is a large strip of parameter space corresponding to adiabatic solution and no solution for large mixing angle region. The non-adiabatic region still remains as a solution but shifted and larger relative to the regular MSW.