Perhaps we could take one step at a time.
Assume our theory of gravity includes gravitons, which are the particles that mediate the gravitational force.
If this gravity gives rise to more gravity, would that not mean that graviton A must be able to give rise to graviton B, such that the energy of A+B is greater than the energy of A alone
The problem is you keep trying to bring it back to ONE graviton sitting there which is by itself stable, in the same way a car sitting on a hill can be stable. This isn't the problem the next step is.
If I give the car a push then I get a problem. So lets do the same I push more energy into the fields near the graviton such that another graviton appears BUT now my two gravitons must also attract each other.
Mathematically:
X energy gives rise to the first graviton
2X energy gives rise to two gravitons as we have quantization
BUT if two gravitons also attract each other, you now go into runaway.
What we can look at is the strong force in the nucleus which also has a self interacting property and it's force carrier particles the gluon. So what stops runaway in that situation you may ask?
Well the force is opposed by the electromagnetic force repelling the protons. So our nucleus at this level is viewed by the electromagnetic force of the protons trying to push each other apart and opposed by the strong force trying to pull it together.
See the difference there is something opposing the self interaction. Compare that to gravity.
Quarks don't appear free in nature, because their force does not diminish with distance, as you separated two the force between them quickly heads to infinity. What is predicted is color confinement which prevents such a thing.
So what you are probing is a particles self energy and how that relates to energy in general (
https://en.wikipedia.org/wiki/Self-energy).
For a graviton you can't do that problem in classical physics because how do we determine the gravitational field of a particle, since under Heisenberg uncertainty principle we can't know the position and velocity together.
