It's also important to present your rationale along with your initial offer. Doing so after the fact could be too late. Inspection reports, contractor estimates, photographs, etc. that provide additional support for your cause may also be helpful.
Banks generally go with the best information provided to them about the property: agent opinion, BPO's, appraisals, etc. As long as you are reasonable and making only necessary or essential repairs and can justify them...there's no reason why they shouldn't consider your well thought out and documented requests.
Best of luck,
If it is an REO, the bank wants you to have a Realtor representing you.
Your Realtor is there to advise you about things like this.
Your Realtor will do a CMA to determine the Market Value.
Chances are; the house is priced at about M.V.
If your's is the only offer; the bank probably won't come down, (in this Market).
If they have Multiple Offers; you will probably have to go a lot higher; certainly not discounted.
But, this is what your Realtor is for.