I won't say I'm an expert, but I've tried numerous variations so I do have a breadth of experience.
A typical second run wine is for every 2 gallons of wine from the first run, add: 1 gallon water, 2 lbs sugar, 1 tsp acid, 1/4 tsp tannin. The quality of the wine will vary directly to how much the first run was pressed. The harder it is pressed, the less "oomph" there is remaining in the pomace. The grapes have only so much to give, and if it all goes into the first run, there's nothing for the second run so a "meh" wine is produced.
My results by year:
2019 -- made standard second run wine from pomace of 15 total lugs Merlot, Zinfandel, and other Bordeaux grapes. I pressed the first run lightly and got a seriously good wine from the second run. I segregated the final pressings -- some was used for barrel topup, and the last carboy was bottled as-is. That wine was good for 4 years, which is about double that might be expected of a second run wine.
2020 -- Did the same with 16 lugs Bordeaux grapes, but pressed the first run harder. I have a basket press so pressing depth is by eye. This second run turned out ok, but was second rate. I used most of it for cooking.
2021 -- made only kits, so no second run wine.
2022 -- tried something different, adding the pomace from 8 lugs Grenache to a FWK Tavola Merlot kit. Did the same with 8 lugs Tempranillo. This came out rather good, the Grenache more so than the Tempranillo. The pomace had enough oomph that the Grenache/Merlot has a lot of Grenache flavor. The final result of this is that I'm unlikely to make a second run wine with water again.
2023 -- Added the pomace from 20 lugs CF, CS, and Merlot to a pair of 23 liter Sangiovese juice buckets. That ratio of pomace to juice was high -- it was hard to "punch down". We also pressed rather lightly and grossed just short of 24 gallons, which spent 12 months in barrel. The result was bottled last month and is stellar. Note that this wine is essentially half Sangiovese, half from the first run.
2024 -- Added pomace from 300 lbs each Chambourcin and Chelois (purchased from
@VinesnBines) to a pair of 23 liter Pinot Noir juice buckets. We apparently pressed harder, and grossed 17 gallons (this is not a problem). This wine is totally green but the post-pressing tasting is positive, and is now in barrel until next fall.
So ... my advice is that if you pressed the pomace hard, don't expect much from a second run wine made with water. Adding it to a kit should produce positive results, although it will vary depending on how hard you pressed, and how much pomace you have with respect to the kit or juice bucket.