In this paper, we consider the problem of spread pilot design and effective channel estimation in multiple-input multiple-output Zak-OTFS (MIMO-Zak-OTFS) with superimposed spread pilots, where data and spread pilot signals are superimposed in the same frame. To achieve good estimation performance in a MIMO setting, the spread pilots at different transmit antennas need to be effectively separated at the receiver. Towards this, we propose a spread pilot design that separates the pilot sequences in the cross-ambiguity domain and enables the estimation of the effective channel taps by a simple read-off operation. To further alleviate the effect of pilot-data interference on performance, we carry out turbo iterations between channel estimation and detection. Simulation results for $2\times 2$ and $3\times 3$ MIMO-Zak-OTFS with Gaussian-sinc pulse shaping filter for vehicular-A channel model show that the proposed pilot design and estimation scheme with three turbo iterations can achieve very good estimation/detection performance.