Some of this can depend how old and what generation/model your SLI-80 is. If you don’t know, check the serial and call Cary and ask. There were a few nice changes/upgrades over the years and outside vendors who created their own series with upgrades, i.e. F1, and even those can be upgraded again. For example, is it a Base model or Signature model, are any of the factory upgrades applied over the years, i.e volume control installed, signature wiring yes/no, how old are those Ruby 6550s, etc. This depends on how you want to attack it, piecemeal -or- possibly go for the whole batch of common upgrades all at once (I recommend this approach, so worth it).
Many of us here could likely go on for pages here about all of the things to look for and try, dare I say send it to Cary to test and apply upgrades, or better yet find a really good local tech to test it. For example,, look over at the caps/age installed, test the tubes/transformers, and more - inside. A really good tech can quickly assess it and speed you forward fwiw. Good techs do this quite regularly.
I owned a fully factor upgraded Signature, then had a local tech buddy help me discover more upgrades replacing caps again, a few diodes, better Silver wiring inside, then tried a few different quads of KT88s, various vintage input/driver tubes, and 6SN7s. I think upgrading to the really good coupling capacitors and [new] main output tube changes made the most notable differences to me in one shot. Get this - Cary actually bought my SLI-80 back from me for more than retail price to study the upgrades we did. The new owner was absolutely thrilled with it. Ended up going with a SLP-98 preamp istead and separate amps. That souped up SLI-80 was sweet, should have hung on to it actually. Again, mine was already a Signature model to begin with. Seriously, I’d just seek a great tech if you want to cut to the chase and start enjoying it more, sooner. It’s worth testing/upgrading if you can. Best of luck.