So both the 0/1 subset sum problem (find a subset of given numbers that add up to a target sum) and the subset sum problem with "multiplicities" (find non-negative integer coefficients for the set elements so that the linear combination of set elements equals a target sum) are NP-complete. Is there some fairly easy reduction from 0/1 subset-sum to subset sum with multiplicities? This seems perhaps non-trivial, because just because there is a solution with multiplicities doesn't mean there is a 0/1 solution.
Some ideas I had that don't seem to work: For element $s$, solve the subset sum with multiplicity problem both for total sum $S$ and $S-s$ with element $s$ removed from the set. Then try to argue that $s$ either is or is not included in the 0/1 solution depending on the answer.