The aim of this paper is to find the transformation for the coefficients of an $N$-linear connection on $E=Osc^2M$, by a transformation of nonlinear connections, to define in the bundle of accelerations the general conformal almost symplectic $N$-linear connection notion and to determine the set of all general conformal almost symplectic $N$-linear connections on $E$. We treat also some special clases of general conformal almost symplectic $N$-linear connections on $E$.