I bought a used bike, it has a set of specialized tires, 27 x 1 1/4".

I was hoping to stick a pair of 700c x 32mm on them.

Do you think this is possible? The rim says it's an ambrosia and has 27 x 1 1/4" stamped on it along with 630 x 18 .

It looks like there is a bit of room for a bigger width tire. Not sure about height, can I adjust where the brakes sit on the frame to accomodate the smaller 700c?