Converting a Two Unit to a 4 Unit in R-2 Zoning

So I'm looking at trying to convert a two family to a 3 or 4 unit.  It is zoned R-2 however with in 500' of the property there are a few 3 and 4 units AND a big apartment complex.  Now I know at first blush the town will say your zoned R-2 so you can't however when I see these other buildings with multiple units I ask myself well why them and not me?

There is one street a few hundred feet away that has 5 three unit triple deckers all side by side and right across the street are some brick 4 units that I believe are owned by the town for elderly/low income housing so why would I not be able to convert my two family, literally across the street, from a two to a four unit?

This is in Woburn just in case it matters.

Tks JD