The Higgs isn't like some sort of "mass coin", particles don't have mass by containing one or more instances of a Higgs boson. Instead there is a Higgs field which individual particles couple to which gives rise to mass. The Higgs boson is an excitation of the Higgs field the same way a photon is an excitation of the EM field, a graviton is an excitation of the gravitational field, etc.
90-99% of the mass in regular matter is due to strong force interactions. In things like protons, neutrons etc the Higgs is only responsible for a small amount. See [1] for a little more detail.
As a quick aside, gravitons aren't quite kosher science yet. We haven't observed them, and we don't even have a coherent theory of how they would work. Something to do with equations being non-renormalizable, I don't claim to understand any of it.
