This paper presents an extension of the L1 adaptive output feedback controller to Multi-input Multi-output (MIMO) systems in the presence of nonlinear time-varying uncertainties without restricting the rate of their variation. As compared to earlier results in this direction, a new piece-wise continuous adaptive law is introduced along with a low-pass filtered control signal that allows for achieving arbitrarily close tracking of the input and the output signals of a reference system, the transfer function of which is not required to be strictly positive real (SPR). Stability of this reference system is proved using small-gain type argument. The performance bounds between the closed-loop reference system and the closedloop L1 adaptive system can be rendered arbitrarily small by appropriate selection of the underlying filter and by reducing the time-step of integration. Simulations verify the theoretical findings.