This is a tough idea. To do it properly would be a big project.
However, as a mod with judicious use of scripting, I think there's some hope. But you'd still have to reinvent a lot of stuff.
Either way you'd have to adjust the graphics engine to render as part of the screen. Either way you'd suffer slowdown because you'd radically increase the number of state changes. I suspect this could be optimized dramatically but would require digging around the graphics rendering code and would be a gnarly, involved process to not introduce bugs.
But if you throw out the HUD and keyboard controls you save yourself a lot of work.
If you wanted to do this for a mod and have it be a project that's of the size that you could reasonably expect it to get done:
(1) Rework game_render_frame to render only to a specific subset of the screen. For future requests, you probably want to make it capable of an arbitrary number of subframes.
(2) Switch off the HUD and disable the keyboard controls involved in manipulating the player's ship. I know there's been some progress in making the HUD more customizable, but I'd be surprised if it's extensive enough to make this doable.
(3) This leaves you with escape, the function keys, and the capability to render 'subframes'
(4) Associate the 'player ship' with some bogus thing. The goal is to invoke the player ship as little as possible.
(5) Configure a HUD with scripting for the subframes you want. Any 3D->2D stuff will likely be messed up (eg rotating/projecting vertices). But you can do ship status and objectives and a crosshair.
(6) Map the controls to joysticks (Has somebody implemented this in scripting yet?

) to move two technically-AI ship, fire the weapons, adjust the speed, fire afterburners, etc.
This ruins a lot of stuff with scoring, difficulty, AI, etc. The controls will be borked and you'll likely have to reimplement a certain level of movement interpolation. But it does give you split-screen control of ships that you could use for a console-style deathmatch thing.
Bonus RoundI vaguely remember being concerned about RTT and game_render_frame when I was doing the scripting for mainhall backgrounds being rendered with a level. If I was concerned enough, I may have tried to make RTT work for game_render_frame.
If RTT
already works for game_render_frame, all you'd have to do would be:
(1) Set a render target
(2) Set a camera
(3) Render the frame
Repeat for each subframe.
Then have the 'real' camera pointing at a 'ship' with the textures for each subframe.
I'd expect this to be horribly inefficient.
EDIT: This handles the problem of rendering, but not of controls/HUD. For that you'd have to use my above suggested approach.