Raise the rent
This actually happens in the art world; there's a guy who goes out of his way to overpay for Warhol paintings, because a) he can corner a finite market and b) when a Warhol painting sells for a record amount, the value of his entire collection goes up even if he's the buyer.
It is possible that Boston houses are underpriced, but it is also possible people will start looking elsewhere. Probably have to dig into income trends and more data rather than just “Boston has limited housing, so it will always be rentable/sellable at a higher price”.
Not something you can do with a house, I grant you. You'd more likely end up in a bubble situation where property just churns through the hands of investors until the bubble pops and someone is left holding the bag.
Hence attempting to buy all the houses is an impractical business plan, unless, of course, it becomes possible as a side effect of government mismanagement.
The Warhol example is fundamentally different, as Warhol isn't painting any more.