smc

First, we need to recognize that a number is going to be largest only if, of the $3$ factors, two of them are small. If we want to make sure that this is correct, we could test with a smaller number, like $30$. It becomes much more clear that this is true, and in this situation, the value of $I+M+O$ would be $18$. Now, we use this process on $2001$ to get $667\ast 3\ast 1$ as our $3$ factors. Hence, we have $667+3+1=\boxed{671}$.