Building over a small creek

I have an old cottage on post and pier and a creek runs next to it about 10' away. I would like to do a small 15 x 20 master bedroom and bathroom addition off the side of the house on the main level. It would be just a single level and, by the way, the creek at this area is underground in a culvert. My thoughts would be to jack up the house and pour a foundation at the same time as this addition. If the 2-3' wide creek is an issue with the city, could I run a beam across the rest of the house when I jack it up (24' width house) and cantilever the addition or perhaps run over the creek and put in a post for a beam about 20-25' feet away from the house. I'm just looking for a little out of the box thinking to solve this little problem. By the way, about 50' away, the creek (still in a culvert) heads under the street and into the ocean. So the city itself has built over the creek with a road and I feel that I should be able to as well. My house is 1900 sq ft and this would add about 300 more sq ft to the total. Thank you for your creativity. Steve