The generalized Fermat conjecture with coefficients supported on a finite prime set

Let $S$ be a finite set of primes. Consider integer solutions $(a,b,c,x,y,z,p,q,r)$ of the generalized Fermat equation $eqref{eq:genfermat}$ satisfying $\gcd(ax,by,cz)=1$, $p,q,r>0$, and $1/p+1/q+1/r<1$, with every prime factor of $abc$ belonging to $S$. Finite-support generalized Fermat conjecture. For every finite set $S$ of primes, there are only finitely many such solutions. This is presented as another conjectural finiteness statement implied by the abc philosophy, allowing the coefficients to vary while restricting their prime support. Its status is not specified in the supplied text.