  A general analysis of line defect renormalisation group (RG) flows in the
$\varepsilon$ expansion below $d=4$ dimensions is undertaken. The defect beta
function for general scalar-fermion bulk theories is computed to
next-to-leading order in the bulk couplings. Scalar models as well as
scalar-fermion models with various global symmetries in the bulk are considered
at leading non-trivial order. Different types of potential infrared (IR) defect
conformal field theories (dCFTs) and their RG stability are discussed. The
possibility of multiple IR stable dCFTs is realised in specific examples with
hypertetrahedral symmetry in the bulk. The one-point function coefficient of
the order parameter in the stable IR dCFT of the cubic model is computed at
next-to-leading order and compared with that in the IR dCFT of the Heisenberg
model.
