You are right.The grease compatibility tests are done as per ASTM D 6185 in which Penetration, drop point and high temperature tests are done on 90:10,10:90,25:75,75:25 and 50:50 mixtures of greases.Depending upon the criticality of application Tribology tests are also recommended.
Normally,if the bases are same they should be compatable.
There is also a chart showing which grease is compatable with other grease.
Thanks