T connection of two Beams To Support 2nd Floor - Post or No Post?
Can it be done? Sure. Is it practical? - you'll need to discuss with the engineer and consider the impact on your budget.
Basically you will need to increase the strength (and usually the size, to get that strength) of the beam that crosses the space so that it can support the beam going down the middle of the extension. Likewise, it will require a sufficiently strong connection to support that load, which may be more complex/expensive than simply supporting it on a post.