polynomial ring variable limit workaround

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On my machine, the maximum number of variables allowed in a polynomial ring is 32767. For instance,

S = PolynomialRing(QQ, 32767,'s')

works, but

S = PolynomialRing(QQ, 32768,'s')

does not.

Is there a workaround with enough functionality to allow me to do something like compute a primary decomposition of an ideal?