We study Stokes phenomena of the k × k isomonodromy systems with an arbitrary Poincaré index r, especially which correspond to the fractional-superstring (or parafermionic-string) multi-critical points ( p ˆ , q ˆ ) = ( 1 , r − 1 ) in the k-cut two-matrix models. Investigation of this system is important for the purpose of figuring out the non-critical version of M theory which was proposed to be the strong-coupling dual of fractional superstring theory as a two-matrix model with an infinite number of cuts. Surprisingly the multi-cut boundary-condition recursion equations have a universal form among the various multi-cut critical points, and this enables us to show explicit solutions of Stokes multipliers in quite wide classes of ( k , r ) . Although these critical points almost break the intrinsic Z k symmetry of the multi-cut two-matrix models, this feature makes manifest a connection between the multi-cut boundary-condition recursion equations and the structures of quantum integrable systems. In particular, it is uncovered that the Stokes multipliers satisfy multiple Hirota equations (i.e. multiple T-systems). Therefore our result provides a large extension of the ODE/IM correspondence to the general isomonodromy ODE systems endowed with the multi-cut boundary conditions. We also comment about a possibility that N = 2 QFT of Cecotti–Vafa would be “topological series” in non-critical M theory equipped with a single quantum integrability.