Increasing under market rent

[Bobby Balentine]

Hello all! I am new to real estate investing. I have my first contract on a large single-family home that was converted into a triplex. A little information before I get to the question. The current landlord does not seem to have good records for the property. (ie maintenance/repair or capital improvements). I know that the roof and siding have been replaced within the last 2 years and a furnace is being replaced at this time. Other than that, no more information. There are 3 separate units (1-2bed/1bath and 2-1bed/1bath) but they are not metered. The landlord pays all utilities. The units rent is $550 for the 2 bed and $475 for each 1 bed. According to biggerpockets BP insights the rents should be closer to $700. So, the question would be if I took possession of the property in say April and they are on a month-to-month lease, when would be a good time if any to increase the rent to market value and would you do one big jump or stagger an amount over time to get there?  Are there any other insights or things I should be thinking about?  Thank you in advance for your comments and help in this situation.