jmc

The sum can be rewritten as $113X+10Y$. To get the largest possible sum, we maximize the hundreds digit, $X$. If $X=9$, the sum is a $4$-digit number, so we let $X=8$ and $113(8)+10Y=904+10Y$. To continue maxmimizing this sum, we can let $Y=9$, a different digit from $X$, and $904+10(9)=994$, which has the form $\boxed{YYZ}$.