No multiple grid is not possible, as you said you can have multiple database installations, example under 12c grid infrastructure, you can have clustered 11g and 12c database, but make sure that your grid and asm should be on latest version.
Also keep in mind Your version of the grid infrastructure should be higher than the databases it serves.
You can not have multiple GI running on same server.
Please review the following note:
11gR2 Clusterware and Grid Home - What You Need to Know (Doc ID 1053147.1)
11gR2 Clusterware Key Facts
"Only one set of clusterware daemons can be running per node."
Also refer the following RAC faq note and you may get answer for most of question
RAC: Frequently Asked Questions (Doc ID 220970.1)