Here is some hypothetical syntax, you just specify the number of matches on the NEWDEMANDERIDVARS option by specifying more resulting variables.
FUZZY BY=Covar1 Covar2 Covar3 SUPPLIERID=ID NEWDEMANDERIDVARS=Match1 Match2 Match3 Match4 Match5
GROUP=CaseFlag FUZZ=1 2 3 EXACTPRIORITY=FALSE MATCHGROUPVAR=MGroup
/OPTIONS SAMPLEWITHREPLACEMENT=FALSE MINIMIZEMEMORY=TRUE SHUFFLE=TRUE SEED=10.
I have a blog post that goes though an example analysis,
https://andrewpwheeler.wordpress.com/2015/05/20/fuzzy-matching-in-spss-using-a-custom-python-function/. It is for a custom match function, but you can skip that part and replace with your own FUZZY command.