Yes & no.  When one of my cats - Debbie - was 11, she developed a loss of
appetite & bloodwork showed sky-high liver enzymes.  She became very ill,
but a liver biopsy was possible via a core needle biopsy, not a surgical
one.  Ask you vet about this.  My vet knew that there was no way she could
perform a surgical biopsy on Debbie in her weakened condition, so she
referred me out to a vet internist/oncologist (who's a little over an hour
from here), who was able to do an ultrasound & the needle biopsy.

Cancer was ruled out, & the internist/oncologist prescribed a treatment
regimen of Prednisone/prednisolone (might be the steroid your vet has
prescribed) and amoxicillin - which was later changed to Baytril (strong
antibiotic) - her liver was not dealing well with bacteria from her
intestines.  The Pred not only was to reduce inflammation, but also to
kick-start her appetite - which is a different scenario than what you're
dealing with.  A little while later my own vet suggested Actigall, she
checked w/ a liver specialist at Cornell to double-check for its
appropriateness for my cat's particular condition, & that was added to the
treatment.  Over the course of the next 4 - 5 years (daily pills) her liver
values slowly improved, to the point where they were virtually normal.

So... my advice would be to check with your vet on the viability of
performing a core needle biopsy, either in-house or as a referral - it was
not stressful on my cat, who was in poor/acute condition at the time she had
it done.  She was given a muscle relaxant before the procedure, that was
all.  A few hours later, she got her legs' muscles coordination back (after
the muscle relaxant wore off), & was feeling considerably better - due to
the Prednisone revving up her appetite.

Cathy

I have something similar with my cat Nick, though he's only two years
old. He's experienced weight loss over the last few months (from 9.1
lbs to 6.6 lbs)and seems a little jaundiced, he was never obese
(always tends toward the lean side), he eats and drinks normally (I'd
say his appetite is marginally larger), and his bloodwork shows that
_only_ his bilirubin is elevated (about 5 times the normative values
of the place that performed the test), white cell counts, liver
enzymes, blood glucose, etc. all all normal. No vomiting or
salivating. Our vet (I've only been dealing with them for a year or
so) suggests Fatty Liver Disease, but the symptoms don't seem to jive
with what I've read. We're taking him for a second opinion.

James.