Representing data in combination of QAM and BPSK
Let's us take the simple case $2\times 2$ MIMO. Let $y_1$, and $y_2$ be the received signal at the first and second receive antennas, respectively. Then we have

$$y_1 = h_{11}x_1 + h_{21}x_2 + n_1$$

and 

$$y_2 = h_{12}x_1 + h_{22}x_2 + n_2$$

where $h_{ij}$ is the channel coefficient from transmit antenna $i$ to receive antenna $j$, $x_i$ is the transmitted signal from transmit antenna $i$, and $n_i$ is the AWGN at receive antenna $i$.

We can write the above signals in matrix-vector form as

$$\mathbf{y} = \mathbf{H}\mathbf{x} + \mathbf{n}$$

Apparently, there is interference here. So, we need to do some sort of equalization. Let's use zero forcing (ZF) for simplicity. In this case you get

$$\mathbf{H}^{-1}\mathbf{y} = \mathbf{\tilde{x}}=\left[\begin{matrix} \tilde{x}_1\\\tilde{x}_2\end{matrix}\right]$$

where $$\tilde{x}_i = x_i + \tilde{n}_i$$

for $i = 1,\,2$. 

Now, suppose that $x_1$ is 4-QAM, and $x_2$ is BPSK, both have the same symbol time. Will that be a problem? and why? They seem separable to me, and can be detected given that the receiver knows in advance that $x_1$ is drawn from a 4-QAM constellation, while $x_2$ from a BPSK constellation. Actually we do this in OFDM. It's called bit loading, where different subcarriers are modulated with different modulation sizes, and schemes when the CSI is know at the transmitter. Of course in OFDM the symbols are separable because of the orthogonality of the subcarriers, but we can somehow separate the signals in spatial multiplexing, although not perfectly.