While Asymptotic Stability (AS), or convergence to zero error, is predominantly considered in Iterative Learning Control (ILC) systems analysis, such convergence is not always possible. One such case exists in multivariable systems in which access is available to only one measurement channel at a time. In particular, a Two-Input Two-Output (TITO) ILC system is considered. While AS is not possible without measurement of both channels, a weaker condition, ILC stability, is possible using only one output channel and suitable learning filters for this case are presented. A Switched Iterative Learning Control (SILC) scheme is then proposed in which stability is achieved with one output and then the measured output is switched and stability is achieved the other. The process repeats indefinitely. AS of the SILC scheme is shown, resulting in zero asymptotic error. A simulation study is presented demonstrating the effectiveness of the proposed SILC scheme.