  The leading-order contribution of a new boson to the muonic fine-structure
anomaly, which refers to a discrepancy between the predicted transition
energies and spectroscopic measurements of $\mu-^{90}$Zr, $\mu-^{120}$Sn, and
$\mu-^{208}$Pb, is investigated. We consider bosons of scalar, vector,
pseudoscalar, and pseudovector type. Spin-dependent couplings sourced by
pseudoscalars or pseudovectors are disfavoured as solutions to the anomaly due
to the nuclei in question having vanishing angular momentum. Spin-independent
interactions resulting from scalar or vector exchange are also disfavoured
because no parameter space exists to simultaneously fit different atomic states
of the same nucleus. Therefore, we conclude that a `Beyond-the-Standard-Model'
resolution of the muonic fine-structure anomaly is generally disfavoured, and
the first-order solution by a single new boson is excluded.
