Para-Hydrogen Induced Polarization (PHIP) experiments were performed in coupled multispin systems at variable magnetic fields. We studied the magnetic field dependence of PHIP in styrene, which is the product of hydrogenation of phenylacetylene. At low magnetic fields where the spins are coupled strongly by scalar interaction efficient polarization transfer among the interacting protons takes place. The experimentally observed spectra are in good agreement with the simulation, which takes into account eight coupled spins. We also demonstrate effects of nuclear spin level anti-crossings on the PHIP pattern. It is shown that rapid passage through the level anti-crossing enables highly efficient polarization transfer between specific spin orders. In addition, we studied PHIP transfer to 13C and 19F hetero-nuclei. It is shown that hetero-nuclei can be efficiently polarized in a wide field range; in particular, for polarizing them it is not necessary to go to ultra-low fields, which provide their strong coupling to protons. The resulting polarization is of the multiplet type and gives strong enhancements of the individual NMR lines. In general, variation of the magnetic field gives the opportunity for manipulating PHIP patterns and transferring polarization to target spins of choice.