go in on

verb2

1. •
   To contribute money for a joint purchase.

   • As they'd expected, Nino had turned them down when they'd asked their future brother-in-law to go in on the purchase. — 2008
2. •
   To participate in; to join.

   • For example, one veteran officer advised a rookie, “The only reason to go in on a pursuit is not to get the perpetrator but to pull the cop who gets there first offa the guy before he kills him.” — 1981