This paper proposes a novel flexible receiver with virtual channels for overloaded multiple-input multiple-output (MIMO) channels. The receiver applies extended rotation matrices proposed in the paper for the flexibility. In addition, adaptive selection of the extended rotation matrices is proposed for further performance improvement. We propose two techniques to reduce the computational complexity of the adaptive selection. As a result, the proposed receiver gives us an option to reduce the complexity with a slight decrease in the transmission performance by changing receiver configuration parameters. A computer simulation reveals that the adaptive selection attains a gain of about 3dB at the BER of 10^-3.