  We prove a priori estimates for a generalised Monge-Amp\`ere PDE with
"non-constant coefficients" thus improving a result of Sun in the K\"ahler
case. We apply this result to the deformed Hermitian Yang-Mills (dHYM) equation
of Jacob-Yau to obtain an existence result and a priori estimates for some
ranges of the phase angle assuming the existence of a subsolution. We then
generalise a theorem of Collins-Sz\`ekelyhidi on toric varieties and use it to
address a conjecture of Collins-Jacob-Yau.
