Have not heard of grafting mopheads. Some Canadian posters have previously indicated they had a commercially obtained, grafted panicle hydrangea but in the US, I have not seen grafted panicles. I have seen mopheads sold as 3 in 1 but these were three distinct varieties in the same container. As mopheads tend to be sensitive to soil pH, consider using a white bloomer too to get variety of colors. Post to keep us abreast of your experiment. Try to use varieties of similar size and vigor. Could include a lacecap too.

Hydrangeas can be grafted but I doubt very successfully in the way you describe. The only grafted hydrangeas I am aware of are tree-form paniculatas and they are top grafted to a clear trunk to provide height and achieve the tree-like form. And to short cut the normal process, which can take several years to achieve. I've never heard of this done with shrubs or multiple cultivars at one time.

Hydrangeas are relatively easily grown from cuttings, so you could take cuttings of several different types to get that multicolored effect and once well rooted, plant them together as a single shrub. Be aware that soil chemistry will affect the coloring and could limit the multicolored effect.