[Just Sold]

You can add on to any building and what it involves depends on how you want to attach it and blend it into the original structure.

Tearing down a cottage and putting up a new one may be cheaper sometimes but remember your property taxes will take a bigger jump for a new building than for a remodeled one. New construction vs old with additions is valued higher.

There are many factors to consider when raising a property to put in a full foundation or even a 1/2 depth one:
First you will be warmer because the foundation will reduce cold and moisture penetration.
The cost of tearing down and a new design doesn't come cheap with disposal and permitting costs. Re-desiging isn't cheap either but should be less.
Putting in a foundation under a cottage costs too. The last one I was involved with on a friends waterfront cottage was about 32K for a 30' x 30' cottage. That was 4 years ago.
Another person I know altered the land in front to put a foundation under his cottage. He is still awaiting the fines and what the state wants him to do to restore things. The cottage basement sits unfinished as he waits. Altering the land for the 1st 50' from the water is a big no no.

If it were me I would put a foundation under the original cottage and add to the rear or side. Remember it always costs more than you or your builder/designer estimates.