It is possible.
But I (and many others) do not recommend it.
Besides keeping track of and updating the common families in two or all of the branches, you would also be maintaining 4 set of place hierarchies, sources and citations.
When needed, if you want to run a report on any one of the branches, that can easily be done from the single database.
But, if you want to proceed, I recently showed how to create a series of filters to identify all of the relatives of a person.
You would use each of the grandparents in the filter and create an export of that person’s branch.
Use the Gramps XML export, use the with media option if each database will have its own media folder, select your branch filter in the People filter (it will be the last filter I demonstrate), and select the References filter Do not include records not linked to a selected person.
Import these exports into a new empty tree and you will have new databases for each grandparent.