Is there a recommended separation distance for multiple vent stacks, such as one for pressure relief, one for ventilation, and another dedicated to purging?

Vent stacks and building ventilation systems are different and should be analyzed/designed differently. NFPA 2 has different location requirements for vent stack and ventilation system outlets. There are code requirements for elevation, distances from exposures, and between exposures. 

There are no specific regulatory or code requirements for vent system separation distances. These should be evaluated as part of a hazard assessment. A primary consideration is that a fire on one should not lead to ignition of another stack which might also be venting at the same time. Dispersion analysis can be performed to ensure that there is adequate separation. Additionally, the vent and ventilation system exhausts should not be able to be pulled into an air intake.