In the midst of some DIY and about to install my first hardwood floor!Super exciting, however I have run into an issue and need some assistance. I am installing 3/4 solid oak flooring. I have a fiber backed w/vapor barrier under-layment for moisture coming up from the unfinished basement. I am off an 1/8 in on my three existing floor heights from other rooms. Can I add an additional 1/8 under-layment to even this out? or will that lead to bounce or other issues. Thank you in advance for your input

it would be better to us some type of wood shim to make up the difference . Cedar shingles can work well or sometimes , I just rip a piece of scrap wood on my table saw to get the shim size or taper that I need .
Adding too much underlayment usually isn't a good idea . It can bunch up on you and twist the board or create bounce as you alluded to .

Eighth inch plywood will be a good shim. Glue the area down with a good latex sub-floor adhesive and use a three-eighths inch staple with a hammer tacker to hold it down while the glue dries. If the sub-floor is fastened down well you will not get any bounce. A ¾ inch hardwood floor fastened with 2 inch fasteners will be held in place well as the fasteners will still penetrate into the sub-floor almost an inch fastening the flooring and the shim in place.
I have used roll roofing, mineral coated asphalt saturated felt, or now asphalt saturated fiber glass, to shim up whole rooms about an eighth inch without gluing it down and had no problems over the last 35 years. Asphalt saturated felt will not compress unless it melts in a fire. I don't recommend adding over a quarter inch, or two layers of the roofing felt.