no, I mean the first stage is differential stage, the second is also differential in stage.
for example instead of using differential stage in the first stage then class a in the next to get two stage OTA
One reason why you would go for a differential pair as the first stage of the opamp is that it provides you common mode rejection. You can use another differential pair to amplify the output of the first pair, but it is not really required as a simple common source gives you similar gain. Since, the common mode is rejected in the first stage there is no need for another stage which rejects common mode.
I believe if the output is taken differentially, then the second stage being a simple common source will not affect PSR. On a different note, with the differential pair as the second stage, and assuming that it is the output stage also, the output swing limits will be smaller compared to common source.
I have found that some comparator circuits uses two differential stage one after one to get high gain, and from here i got the idea to do this in normal operational amplifier
the first stage is fully differential output and the second one with single ended output
I know this is an old post, but just wanted to add a comment. In designing multi-stage amplifiers, using diff to diff to diff and repeating has become common in designing amplifiers up to 7 stages reported by ADI last year at ISSCC and still resulting in a stable design. I have designed my self up to 5 stages, taped out and it works like a charm! see attached image.