I wonder if Swedish requirements could coincide with ROKAF requirements for the 2030s, and if they could actually do something together. Both have expertise designing and producing 4.5th gen fighters, have domestic industrial bases, have cooperated in defence before, have negotiated for joint development of KF-X in the past (and Sweden assisted subsystem development), both are very much developed economies but lacks critical mass/gross economic size to finance next gen fighter development alone but still wants 5+ gen fighter for the near future. Also, both are directly facing its adversary at it's vicinity (for Sweden it's Russian forces in the Baltic/Kaliningrad/St. Petersburg and defence of Finland as NATO ally, whereas for ROK it's DPRK directly above it and Chinese forces just across the Yellow Sea. Very similar operational environments, especially the distance, if you ask me). Korea's also developing the engine for the next gen fighter so that could be very attractive prospect for Sweden as well.
I think Sweden delaying future fighter related decisions to 2030s could actually turn out to something beneficial for both countries. Be it a joint programme based on KF-X block III or a clean sheet KF-XX/whatever they would call it in Sweden, or just a joint development of individual subsystems and adjuncts, I think both countries could work it out. Most importantly, I think it's important to note that all countries capable of developing their own fighter jet are already up to something be it GCAP, NGF, KAAN or AMCA.
Though I wonder if Sweden would try to stick to a light-weight single engined design for 5+ gen fighters like the FS2020. This might be the biggest disagreement if there is to be any serious talks.