When n is negative or 0 in reachNFloorSet(), you're returning 0 or 1, but you should be returning sum or sum + 1. Otherwise you're throwing away all the accumulated info.

It would be better, I think, to rewrite your method so it doesn't have to worry about how many steps have already been taken:

public static int reachNFloorSet (Set<Integer> numbers, int n) {
    if (n <= 1) {
        return 1;
    }

    int sum = 0;
    for(Integer x: numbers) {

        if (x <= n) {

            sum += reachNFloorSet(numbers, n-x);

        }
    }
    return sum;
}

You don't have to worry about n being negative, because you don't make recursive calls where that could happen.

When n is negative or 0 in reachNFloorSet(), you're returning 0 or 1, but you should be returning sum or sum + 1. Otherwise you're throwing away all the accumulated info.

It would be better, I think, to rewrite your method so it doesn't have to worry about how many steps have already been taken:

public static int reachNFloorSet (Set<Integer> numbers, int n) {
    if (n == 0) {
        return 1;
    }

    int sum = 0;
    for(Integer x: numbers) {

        if (x <= n) {

            sum += reachNFloorSet(numbers, n-x);

        }
    }
    return sum;
}

You don't have to worry about n being negative, because you don't make recursive calls where that could happen. (Of course, you should guard against negative n in the original call as well.)