I am new to this, and I am hoping to supplement my current income so I don’t have to work so hard in the hospitals.

These would be a supplement to your BHA and also provide cash flow once you move on to the next duty station. 

The only reasonable explanation I can find is they are supplementing with J.O.B. income, or perhaps living off the excess borrowed funds..Some part of their story is missing.

I'm hoping to earn some extra income to supplement my day job.

If that's not an option, getting a side hustle to supplement income could also work.

Other houses that I have that are strongly cash flowing I can use to supplement my income and help with operations costs when starting into the MF property.I have also invested in a pair of fourplexes, which is not quite the multi-family model (which is 5+ units) but a good starting point with a larger supply of units so a vacancy does not hurt quite as much.

So the question becomes, are you more interested in cash flow to supplement you income or are you more interested in real estate appreciation for a larger sale value?

I’m happy with supplementing monthly expense down to triple digits, or realllly low 4-digits.

BRRRR is common in commercial and your existing lender will need more of an appetite for a refinance if they know that they are going to loose the loan.Fannie, Freddie, and some local/regional banks actually have a supplemental loan feature that facilitates a BRRRR...the original loan stays in place and you get a supplemental loan when the property has been re-positioned, rents raised, and stabilized.There are also construction/perm loans where rehab is financed during the IO construction period and then the loan starts amortizing later. 

I am a financial independence "enthusiast" if you will and always interested in adding more semi-"passive" incomes streams to supplement my current investment portfolio (mainly index funds at the moment).