My prefix has a classy house, where no one lives.
My infix is a sneaky vermin.
My suffix is the past of consumption.
What am I?
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OPERATE
My prefix has a classy house where nobody lives
An Opera House is a classy house where nobody lives
My infix is a sneaky vermin
A sneaky Rat.
My suffix is the past of consumption
Consumption = Eat, whose past tense is Ate.