In this paper, we consider adaptive transmission for quasi-orthogonal space-time block codes employing 4 transmit antennas. Orthogonal space-time block codes provide full transmit diversity and are an efficient means to reduce the negative effect of fading channels on the wireless link performance. However, these codes cannot provide full symbol rate with more than two transmit antennas and orthogonality has thus to be sacrificed in order to achieve the high data-rates promised by MIMO systems. We propose a closed-loop mode for two quasi-orthogonal space-time block codes with symbol rate 2 that aims at reducing the performance degradation caused by the loss of orthogonality. The feedback scheme is based on partial channel state information available at the emitter. The performance of the adaptive modes with various detection techniques over a Rayleigh flat-fading channel is assessed by means of numerical simulations.