Should I use "multiple" and "at once" in one sentence?

Solution 1:

It seems that there's nothing wrong in this phrase, as long as "multiple" refers to the noun "services".

Solution 2:

At once has at least two different, but related meanings

1 at the same time : simultaneously

2 immediately

While your usage may be comfortable with both, there could be circumstances where the immediately may be understood, but where you wanted to focus on at the same time.