Without seeing more details of the (hypothetical) deal, it's difficult to get exact numbers for you. That being said, it would be possible to use private/hard money to purchase the entire portfolio wrapped up into a single loan as long as all of the relative values make sense.
Are these properties already rented and performing, or are they needing rehab work to get them up to rent worthy condition?
How much value is built into the deal? (What is the ARV in relation to your negotiated price?)
If the deal is solid, and you as a borrower meet the basic lender's qualifications, the process should be pretty quick and easy.Get the properties under contract, collect all of the information regarding the deal, pitch it to lenders, negotiate terms/rates if possible, and then send the package to title for closing. This is bearing there are little to no repairs needed. If repairs are needed, a scope of work will need to be written up to provide with the presentation as well.
Hope this helps!
Andrew Bowlds - Private/Hard Money Consultant