  Even-parity interorbital spin-triplet pairing emerges as an intriguing
candidate in multiorbital superconductors with significant Hund's and
spin-orbit coupling. Within such a state, the pairing is dominated by the
intraband pseudospin-singlet component via the spin-orbit coupling,
distinguishing it from a pure spin triplet and motivating the name, shadowed
triplet. With atomic spin-orbit coupling, it was shown that this pairing
exhibits an anisotropic $s$-wave character, while higher angular momentum
pairing symmetries such as $d$- or $g$-wave have been proposed based on
phenomenological analyses in candidate systems. A natural question is then
whether higher angular momentum pairings may arise with this form of
spin-triplet pairing. Here, we examine the interplay between spin-orbit
coupling and the electronic dispersions in correlated metals and demonstrate
how they can be realized. We apply this idea to Sr$_{2}$RuO$_{4}$ and determine
the competition among different pairing states as multiple spin-orbit coupling
parameters are tuned. The presence of both $d$- and $g$-wave pairings,
including a $d+ig$ state, are found when momentum-dependent spin-orbit coupling
with $d$-wave character is increased. Implications of the theory and future
directions are also discussed.
