For a "non-recourse" loan you'll pay more in interest & fees & the dynamics of the property will have to be strong.
You'll also have to have a substantial down payment - varies w/ the lender, but expect 20-35%. On $4mil that would be $800K to $1.4 mil. This $ doesn't all have to be yours, but if it is "lent $", the deal will have to sustain those payouts; you'll need commitment letters; in those letters your secondary lenders will have to agree to the positioning of their leinhold (bank will have 1st position & typically 2nd would be next largest loan, etc.)
Most lenders will be willing to look at your deal - make sure you've made it look good - would you invest your retirement $ in this deal?
I'd start w/ a banker that you have a relationship with. They may not do the deal, but they should be able to tell you why not & critique your proposal. They should be able to give you contacts of who might consider your deal.
You didn't mention whether you had a specific property in mind. THIS IS HUGE!!!.
If you have a property in mind, your presentation can be much more specific on how you will turn it around,
If you are looking for shopping $, the bank can give you parameters for a deal they would consider.
In my experience, if you are shopping, find out a few bank parameters, then find your deal. If your deal is solid, your plan is solid, you &/or your management is solid, you can shop your financing & get your deal done. If you have no experience in this, private $ may be your best option. Expect to give up a piece of the pie long term in addition to the financing. If your deal is not strong enough for that, it probably isn't a deal.
If you have a property in mind, I can review it for a fee. If you don't, but want to begin investing, call me to take what I call a "temperature test" so I can make recommendations on how to proceed.
Sincerely - Ken Clay - Clay's Castles Real Estate (336) 782-1237