Technically, I believe so. Someone can correct me if I'm wrong. In reality, you can keep increasing rent by the max annually. And often those increases will outpace the market and the tenant will leave on his own. But it is standard practice in real estate for landlords to offer existing tenants financial incentives to move out.
@Sienna remember PGFHGS.
In Israel, they have an expression בכביש אל תהיה צודק, תהיה חכם (and I'm not sure that in this specific case you are צודק).
The fact that the previous landlord didn't regularly raise rents is a problem, and the existing contract should have served as a bargaining point for you to lower the purchase price. At this point you are stuck with it. Raising residential rent by 75% is harsh, even if you have some perceived moral justification (market rates). You should be happy with the fact that the tenant is willing to be somewhat reasonable and agreeing to a 30% increase as stated. Grab it, and offer some kind of compromise or incentive for the tenant to either bring it up to market rate within a reasonable time, or move out.
Allow me to suggest a compromise that might work (I proposed this years ago to two friends of mine where one was the landlord wanting to expand his living space, and the other was a tenant who was there even before the current landlord and was paying below market rent):
Make monthly increases of $200 to the rent. If he moves out within X number of months, he gets back a certain percentage of the increases he paid (the larger you offer as a refund the faster he will move out).
This arrangement might also be too harsh for the tenant, but the gist of it is the point. Let the tenant either ease into market rate, or leave, and give the tenant an incentive to work with you.