Not addressing figs, per se: rootstocks and interstem material does have some affect on the graft material. Some are chosen for the vigor and disease resistance on the roots, others for their ability to dwarf or retard growth of the scion. Not all things are compatible. I have heard of experiences with citrus, for example, when the grafted tree grows fine for about 10 years, and then falls off. Apparently there is a certain amount of incompatibility (rejection) between any given rootstock and scion, and if it is too great, it eventually fails.
Don't know that there is any or much study material on fig compatibility when grafting. Things that are used in commercial orchards have much more study and mush more history on which to judge things. So plums and oranges, apricots and apples, peaches and grapes have mush more info available when it comes time to trial as new variety.
When grafting apples, for instance, is is interesting on a multi-grafted tree to see how the various varieties perform, when all on the same rootstock. Some are more vigorous, some less. The ones that break dormancy first, draw the most sap and will delay bud break and/or suppress other varieties.
A European pear grafted on top of an Asian pear can suppress the Asian pear and delay flowering till late in the summer. Interestingly, when the European pear is grafted on top of the Asian pear, it will break dormancy much earlier, and the sap will flow between the rootstock and the E pear, even tho0ugh the A pear is dormant.
You will have to experiment.