Is it possible to have two internet plans at the same address?

I just moved to a new apartment and would like to keep my current internet plan. When I went to update my address I got the following notification: 

"Another customer has service at your new address, so we have to schedule your installation out at least five days and close your old account the same day you install"

The house is set up for cable internet. Is it possible for us both to keep our current internet plans? Housemates live on the bottom floor, I live on the top. Would be a bummer if I had to cancel mine now as I just paid for the upcoming month a week ago.