Couple of things to consider
- multi GPU creates its own potential bottlenecks copying frame buffer around PCIe bus. Sometimes simply getting a better GPU is much easier/more stable [though yours is more than capable... when used with right settings]
- Consider your target encoding. Up until VERY recently, AMD's H.264 encoding was sub-par (per EposVox and others). For a given higher level bitrate, AV1 is often considered likely to provide better image quality ... but depends on your workflow and target platforms whether that is viable. If you are Recording, editing (re-encoding using std lossy compression) then your video editor workflow comes into play. If you have AMD GPU, you may be better off using H.265.. .depends on specific details
- how long to you want this GPU to last? if a more than 2 years, likelihood of wanting AV1 as an option seems high (if not already)
- though not my area of expertise... plenty of commentary in this forum over the years on default GPU settings, nVidia drivers and associated software that don't play well with livestreaming (at times)... ie, you may need to make changes outside of OBS Studio to resolve your bottleneck
- and you may, or may not, be using appropriate Recording settings for your situation (lots of bad info out there)
So... the issue is that your question lacks enough detail on workflow to provide a decent answer
- as livestreaming; vs Recoding and upload later; vs Record, then edit, then upload each have their own implications
- you did NOT mention preferred encoding format
- you did NOT post your OBS Studio log so others (much more knowledgeable than I could review your settings)
- you did not indicate OS optimizations to reduce hardware resource demands (if such are an issue in your specific case...)
So... you may be well-versed in OS and OBS Studio optimizations, and a 2nd GPU is truly required ... or maybe that isn't required and instead you simply need the right balance of settings (like screen refresh rates, capture rates, encoding settings, etc)