I rent.. and having dogs at all limits your options pretty drastically.. and when you do find some place dog friendly,2 is usually the limit for most places (and if not, there is a combined weight limit that usually tops off at 1 medium/large dog)
The problem is, few places are actually owned by independent landlords in major cities.. usually you have larger companies and rental associations, the rules are set in stone so a little money and extras (training certificates, references etc..) just doesn't do it for most.
Personally.. adding another wouldn't be something I would do. You might be able to squeeze 3.. since it's only one more then the "average" dog limit and your other dogs are already trained, vaccinated etc.. ... but 4 IMO is pushing it. Be prepared to pay more and live further away from popular real estate areas (since honestly, places that are in great locations and have average rent etc... don't NEED to have cushy pet restrictions. So they either don't allow or have tight rules for 1 dog or 2...and refuse to budge more then that, since they have plenty of people waiting to move in regardless)
I would find a place in the area you are searching for that allows the amount of dogs you do have... and THEN consider dog #4 if they are lenient.
I have seen some really sad situations and hard choices being made because someone just CANNOT find somewhere to live that is a reasonable distance and reasonable rent from where they need to be.. and I wouldn't wish it upon anyone. So my advice is, find a place to rent with the dogs you DO have. and once you are already there, then maybe try working the landlord with what a GREAT tenant you are and how you would like another
Just to give you an idea.
Places in Boston to rent.
From those places.. places that allow dogs.
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from that..you aren't even BEGINNING to deal with weight limits, breed restrictions, numbers etc...