First, this setup is a figure from the Gray,Meyer book, not your testbench. I understand if you don't want to share a print-screen, but it will limit the efficiency of solving.
Second, I don't see how you added the additional diff.pairs, this is not a simple unimportant detail I think, now you are talking about an other circuit basically.
Show more information about your circuit, how you connect the additional transistors, maybe you missed a connection somewhere, or how you modified the common-mode feedback (I've just assumed you had to). Or if you don't want to share more, I recommend you to check which transistor is not in saturation when your phenomenon occurs. Non-linearity of OPAmps is strongly connected with decreased open-loop gain, which is connected with devices which entered into triode region. You can set a DC input value and save operating points at that, annotate the regions to the schematic.