I think the closest that you'll be able to get to split screen is playing over LAN and having two monitors next to eachother.
From a technical perspective it's just not viable. Source is only designed to support one player per machine, and the entire optimisation of maps in Source are dependent on the machine only having to render the map from one perspective. Rooms and models that aren't visible from their position are not rendered, and even having two player displays through one GPU would screw this hard.
Also I think the entire code for player control would need to be recoded, as it only allows for input for one player.. it doesn't comprehend more than one user's inputs.
All in all, it would basically require an entirely different game engine, most likely built from the ground up to get a functional split screen experience, and even then 2 player displays would be optimistic at best.