dcasto:
The standard for compressing CO2 and liquefying it in the CO2 industry was, for approximately 70 years, a 3-stage compression cycle starting with essentially atmospheric CO2. I designed, installed and operated over 20 of these reciprocating applications in various countries and the usual conditions were, as I remember:
1st Stage Suction = 1 - 1.5 psig, 85 oF
1st Stage Discharge = 60 psig, 250 oF
2nd Stage Suction = 58 psig, 90 oF
2nd Stage Discharge = 260 psig, 275 oF
3rd Stage Suction = 255 psig, 90 oF
3rd Stage Discharge =1,200 psig, 285 oF
I clearly recall that we never came close to the 350 oF. With leaky discharge valves we developed around 325 oF.
Some of the machines were horizontal, in tandem; others were horizontal, balance-opposed. We were the world's largest CO2 producer at the time and we never used a 4-stage recip for this service because a 3-stage did a good job.
I later took some of these compressors and re-bored the 3rd stage oversize to recycle expanded -10 oF vapors generated by expansion of the HP liquid into 250 psig storage tanks. This allowed me to convert what we used to call High Pressure CO2 process to a Low Pressure (250 psig) CO2 process, storing the LP CO2 as saturated liquid and also storing and distributing it as such.
I don't think your concerns about having to use a 4-stage machine are valid.