Are you a section 8 buyer by any chance?  

In 2018 we began sourcing off market deals by doing direct mail marketing campaigns.

I do not want to reject him based on those grounds and I am considering increasing the rent by $100 a month and letting him move in.

Example: Do it by unit size, every 2 months a different size increase. 

Quote from @Daniel Rabinov: I’m new to REI currently looking to acquire multifamily properties in the North Miami Beach, Aventura, and Hollywood areas that meet the following criteria:Price per Unit: Maximum $250,000 (4 PLEX MAX 1M)Cap Rate: 7.5% or higher as-is not pro formaValue-Add Potential: Properties that offer the opportunity to renovate, improve, and increase rents or overall property value.My focus is on underperforming properties with strong fundamentals that are located in these markets.

I'm sure they moved on to someone else by now.

Update- After dealing with a couple different realtors and submitting offers.

I grabbed the contract and offered 100k less, and got it, Talk about timing.

Start by going to www.narpm.org to search their directory of managers.

Be safe out there and be careful what type of advice you offer your clients.