I am planning a addition on the back of a 2 story colonial.  There will be a full basement, but the addition will be only one story.  The dimensions are going to be 26' x 26'.  Can I pour grade beams to hold the first and second floors of the existing house?  How bout pouring a grade beam to hold up the main floor of the addition (wooden floor).  the grade beams holding the house would have to be secured with a ledger board to the side of the concrete beam to hold the lumber.  What are your thoughts?  If I add a pilaster on each end of the beam and a spread footing under each pilaster. I have full confidence that I can build this.  I am just unsure of the engineering aspects of it.  Can I get away with no columns?

I would ask my engineer about using a frost protected, monolithic, thickened edge slab on grade - ie. no basement and no changes to the existing house foundation.

my house is a garage under. Intend to use the additional basement space as a garage. So I would like to preserve this as much as possible. I could simply buy pre engineered wood or steel beams and accomplish what I am looking for. I was just unsure of what others have done in this scenario or if anyone had tried using concrete as the beams in their house

Lots of buildings have with no problems. Some, like "Falling Water", get it wrong and need very expensive repairs.

That is a a pretty wild house. Don't worry mine won't be anything like that. I will have to do as many calculations as possible and them ask some of my college friends that are engineers