If there is a new tenant, everyone (including children) that meets the standard for being a tenant (whatever the statutory definition is) needs to be on the lease.First, you need to ensure the capacity of the unit is not exceeded (in OR that's 2/bedroom + 1). 

Accepting that some clients wouldn't want a person who is "part time" etc (and I agree that's a fine argument) what are the chances of finding a broker who would be ok working with me in this capacity?

These two are Atlanta locals and have capacity in their multi-family buckets. 

From there it's a personal decision that only you can make.As to the some money better than zero money questions, that's a function of your current capacity and how much profit you are seeing from managing these properties.

What is their capacity to pay current market prices for rent?  

Explain your expectations and ask if they think they are reasonable or what their capacity is for you.

Meanwhile, businesses operating at limited capacity will remain a headwind to increased economic activity.

If the subject property line is within 300 feet of an aboveground, stationary storage tank with a capacity of 1,000 gallons or more of flammable or explosive material, then the property is ineligible for FHA insurance.

Simply lenders can get tapped out from time to time and you don't want to miss out on a great deal waiting for your lender to free up lending capacity. 

A great deal depends on your market but on the whole, small multifamily retains the capacity to be purchased with residential loan and has the economies of scale advantage.