When to implement a CSP? (Merging CRM/Salesforce instances)

Scenario:  Three companies have merged into one newly branded company.  They need to merge their instances of Salesforce or start from scratch (this is currently being worked on with a hired consulting firm to figure out best path forward).  At the same time, this newly formed company knows they need a customer success platform ASAP.  

Question:  Should they implement the CSP first, simultaneously or after the CRM project is completed?