Yes, you can add an insulated ground bar in the can (you should be able to get one specifically designed for your particular can, but here's what they look like):

.. and then connect it to the other ground bar using a piece of #4 AWG (solid bare copper, or stranded THHN insulated) assuming you're still at 200 amps. This guarantees that the green bonding screw that's actually bonding your neutral on the other bar will affect both bars if it is removed. It's common to add these for isolated grounds, where they're connected to a different ground altogether instead of the other bar.

Note - the one you buy may come with its own bonding screw, and the appropriate tapped hole to receive it - so check for that prior to connecting the two together (IOW, read the installation notes that came with it).

Mixing Grounded and Grounding

If this panel serves as the main disconnect, and the grounding and neutral bus bars are bonded. Then yes, you can terminate both grounded (neutral) and grounding conductors at the same bus bar.

^{Notice that the bus bars are bonded using a bonding strap.}

Multiple Conductor Terminals

If the bus bar is able to accept multiple conductors under some or all of the terminal screws, it should be labeled as such either on the bar itself or in the panel documentation. Terminating multiple conductors under a screw that is not rated for it, can cause bad connections, excess heating, damage to the conductors, etc.

Additional Bus Bars

Some panels are configured to allow additional bus bars to be installed. If your panel is one of them, you could install an additional bus bar and terminate extra conductors there. Other panels may accommodate extended (longer/larger) bus bars, that can be installed in place of the existing bus bars.