Lenders are not all created equal. They vary in terms of what they charge to do a loan, what they charge for a certain rate, the programs they offer or whether they approve your application in general. Lender #1 might calculate your income differently than lender #2, which affects the amount you're approved for and/or your DTI, which in turn could affect your rate. Lender #1 might want a 700 FICO on the same type of loan lender #2 will take 680 on, so you could get approved or denied based on the guidelines or overlays of each lender. All of this and I'm not even including what I'd argue may be THE most important thing: level of communication. You can get offered the best rate in the world, but it doesn't do you any good if the lender takes 3 days to return a phone call, text message or e-mail and you don't close your deal.
The first question that popped into my head: is this for a conventional multifamily investment property? If not, the fact that you have to put down 25% is a good example of an overlay. Fannie/Freddie require 15% down on a single family investment and 25% on a multifamily investment....so if this is for a single family and the lender is requiring 25%, that's an overlay. So, you could go to a different lender and they might only require that 15%.
A lender can add additional requirements or make it harder to meet the criteria, but they can't make it easier. If Fannie/Freddie say you need 15% on a single family, the lender can require 20% if they want to, but they can't allow 10%.
Add in nonQM loans and that's a whole different ballgame. Hopefully that helps!