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A future high-intensity e+e- collider running at the Z-pole, while not achieving high energies, offers great potential for BSM explorations through indirect effects. The prospected 6x1012 Z bosons which would be produced on-shell would not only result in a leap in precision for traditional electroweak observables, but are an excellent heavy flavour factory as well. At the same time, experimental runs above the Z resonance up to the tt-threshold will offer different and complementary insights. We explore the implications of precision measurements at FCC-ee in the search for heavy new physics, both within an EFT approach and in explicit models.