There is a question for compression ratio.
What is the range of the compression ratio?
If the value know, Compressor stage is decided it.
Compression ratio as such is not an issue.
What normally sets the maximum compression ratio of each stage is the maximum allowable discharge temperature of each stage. So the first stage compresses to that allowable temperature, then there is intercooling, and then the second stage, et cetera.
If I understand you correct, you have saturated steam of 2.3 kg/cm2g and 136 oC, and you want to compress that up to 15 kg/cm2g ?
But with steam you can not have intercooling between multiple stages because that would condense it all.
So what you want to do is not feasible, in my opinion, because you would need a single stage compressor (without interstage cooling) and that would result in a very high discharge temperature that would be a problem for any compressor.