Even-parity inter-orbital spin-triplet pairing emerges as an intriguing candidate in multi-orbital superconductors with significant Hunds and spin-orbit coupling. Within such a state, the pairing is dominated by the intra-band 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 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.
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