Dipole-dipole interactions lead to frequency shifts that are expected to limit the performance of next-generation atomic clocks. In this work, we compute dipolar frequency shifts accounting for the intrinsic atomic multilevel structure in standard Ramsey spectroscopy. When interrogating the transitions featuring the smallest Clebsch-Gordan coefficients, we find that a simplified two-level treatment becomes inappropriate, even in the presence of large Zeeman shifts. For these cases, we show a net suppression of dipolar frequency shifts and the emergence of dominant non-classical effects for experimentally relevant parameters. Our findings are pertinent to current generations of optical lattice and optical tweezer clocks, opening a way to further increase their current accuracy, and thus their potential to probe fundamental and many-body physics.
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