Based on the multipole expansion theory, we show that a transverse optical torque acting on a dipolar plasmonic spherical nanoparticle can be anomalously enhanced in two plane waves with linear polarization. Compared with a homogeneous Au nanoparticle, the transverse optical torque acting on an Au-Ag core-shell nanoparticle with an ultra-thin shell thickness can be dramatically enhanced by more than two orders of magnitude. Such enhanced transverse optical torque is dominated by the interaction between the incident optical field and the electric quadrupole excited in the dipolar core-shell nanoparticle. It is thus noted that the torque expression based on the dipole approximation usually used for dipolar particles is not available even in our dipolar case. These findings deepen the physical understanding of the optical torque (OT) and may have applications in optically driven rotation of plasmonic microparticles.