  In this paper, we extend a result of Gao Chen regarding the solvability of
the twisted deformed Hermitian Yang-Mills equations on compact K\"ahler
manifolds to allow for the twisting function to be non-constant and slightly
negative in all dimensions. Using this result, we prove that the twisted
supercritical dHYM equation on compact, projective manifolds can be solved
provided certain numerical conditions are satisfied.
