Not quite sure what you have in mind here. Are you suggesting wiring the primaries of the mic transformers in parallel and their outputs in series?
Bear in mind the functions of the transformer are:
1. To match the impedance of the ribbon to the input impedance of the preamp. The impedance is transformed by the square of the turns ratio, so if you have a mic with a 2 Ohm output impedance and a 1:50 transformer, the mic will look like 5 KOhm to the pre-amp. If you set the pre-amp input to be 5 KOhm, i.e. matched to the transformed mic, there will be maximum power transfer and best damping factor on the ribbon, but the volts at the pre-amp (and microphone) will be half the unloaded values. If you want to match the mic to a pre-amp with a fixed input impedance, you need a transformer with the correct turns ratio. Once you have that, no adding of extra transformers will improve things.
2. (as a consequence of 1) To step-up the output voltage of the microphone. The volts are multiplied by the turns ratio.
3. To generate a balanced signal. Most ribbons are not centre-tapped, so the transformer gives a way of generating a balanced signal through centre-tapping the secondary. With care, this could be done with multiple transformers if you had free access to the windings, but you would have to think carefully about phasing.
The upshot of all this is that multiple transformers would only benefit you if (a) a single transformer was not the correct turns ratio to match your mic to your preamp or (b) you didn't care about running unmatched and simply wanted more volts at the preamp.
The disadvantages:
1. Liklihood of not presenting the ribbon with a matched load, so compromising the damping and transient performance.
2. Possible deterioration in signal quality because of non-identical characteristics of the transformers.
3. Increase in system noise due to the Johnson noise of the increased source impedance. In theory, this should be compensated by the increased gain, but in practice it rarely is.
4. Danger of increased hum pickup due to distribution of the transformer function over two (or more) physical transformers.
Does that answer your question?
Let us know how your experiments work out. You will need to listen very carefully to subtle changes in the transient response of the microphone as well as the obvious output level changes and any extra noise (and hum).