  We study a class of topological materials which in their momentum-space band
structure exhibit three-fold degeneracies known as triple points. Focusing
specifically on $\mathcal{P}\mathcal{T}$-symmetric crystalline solids with
negligible spin-orbit coupling, we find that such triple points can be
stabilized by little groups containing a three-, four- or six-fold rotation
axis, and we develop a classification of all possible triple points as type A
vs. type B according to the absence vs. presence of attached nodal-line arcs.
Furthermore, by employing the recently discovered non-Abelian band topology, we
argue that a rotation-symmetry-breaking strain transforms type-A triple points
into multiband nodal links. Although multiband nodal-line compositions were
previously theoretically conceived and related to topological monopole charges,
a practical condensed-matter platform for their manipulation and inspection has
hitherto been missing. By reviewing the known triple-point materials with weak
spin-orbit coupling, and by performing first-principles calculations to predict
new ones, we identify suitable candidates for the realization of multiband
nodal links in applied strain. In particular, we report that an ideal compound
to study this phenomenon is Li$_2$NaN, in which the conversion of triple points
to multiband nodal links facilitates largely tunable density of states and
optical conductivity with doping and strain, respectively.
