A new nonsymmetric bis(aryl-imino)acenaphthene ligand (Ar-BIAN), featured by a subtle steric and electronic unbalance of the N-donor atoms, is reported. With the new ligand and the corresponding symmetrically substituted derivatives both neutral and monocationic Pd-CH3 compounds have been synthesized and characterized. In particular, the series of the monocationic complexes [Pd(CH3)(L)(Ar-BIAN)][PF6] (L = CH3CN, dmso) has been now extended to dimethyl sulfoxide derivatives. The monocationic complexes were tested as precatalysts for the ethylene/methyl acrylate cooligomerization under mild conditions of temperature and ethylene pressure. The catalytic product is a mixture of ethylene/acrylate cooligomers and higher alkenes. The catalysts containing the new nonsymmetric ligand are found to be more productive than those with the symmetric Ar-BIANs. The Pd-dmso catalysts are more productive and show a longer lifetime than their Pd-NCCH3 counterparts.