The new property has to make $50k plus $12k/yr more than the existing property just to break even.

These traditionally have lower rates than cash-out refinances and will only cover your existing loan amount + closing costs, so you'll need an existing mortgage for this type of loan.4.

A 50% LTV on a $120K house at 7%, 30 year Am results in a $400/mo interest payment.The cashflow on your existing duplex goes to $1,000 per month, but now you can buy another just like it so yoru cashflow goes to $2,000 per month.  

This allows you to access funds while keeping your existing mortgages intact.Second Mortgage: Explore lenders who offer second-position loans on investment properties, though rates will be higher.Cash-Out HELOC : While traditional banks often restrict HELOCs on non-owner-occupied properties, some portfolio or private lenders may offer HELOCs for investors.With $15-20K in liquid funds, look for deals where you can negotiate terms:Seller Financing: Negotiate lower down payments or interest-only periods.Subject-To Financing: Assume the seller’s existing mortgage while covering the down payment.Lease-to-Own: Lock in the purchase price while using rental income to build equity.

new construction gets valued at a way higher premium. this is a false statement. new construction will always beat existing Very market dependent.

Unlike refinancing, which involves taking out a new loan, recasting keeps your existing loan terms—including your interest rate and loan duration—intact.

Many European cities have existed far-far longer than the USA has even existed.

Would your existing tenants stomach that much of an increase?

Alot of unknowns as you don't have the ability to walk the property beforehand, but interesting process, and pretty good deals exist there.While the Trustee Sales are cash purchases, there are many hard money options that can turn over the funds in time for the 24 hour funding required to complete the purchase.If you are interested, let me know and I can go into more detail, as well as make some other suggestions for you to consider. 

You can often get better rates with a national lender, but the customer service is non-existent, communication probably sucks, they may ask for the same documents multiple times, etc.