I would wager that the hardware would be able to run 3 instances of the game. Though my experience with running more than one full-screen application on Nvidia hardware is mixed, depending on hardware and drier version. At the very least, you'd be able to run one fullscreen, and two windowed.
There's also the matter of being able to run more than one accoutn at once. From teh website:
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Running multiple EVE clients on same computer
Is it possible to run multiple EVE clients simultaneously on the same computer?
With the Trinity expansion, a new graphical option was introduced to EVE. You now have the option to choose between "Classic" and "Premium" graphics content. Classic graphics content is intended for users with lower-end hardware and that choice uses less system memory than the premium graphics content. Premium graphics content on the other hand is designed for users with high-end hardware and uses more system memory than classic graphics content.
Players now have the option to set some of the clients values themselves, such as cache size, and this comes into play when running more than one client. Lowering said values will decrease minimum memory usage which may enable lower-end hardware to run a single client more efficiently and may enable high-end hardware users to run multiple clients.
Although it is not officially supported by CCP, it is possible to run multiple clients simultaneously. However, doing this has been known to cause some problems with some computers.
When running multiple clients it’s suggested to change the level of cache to “Low” or “None” ( listed under the “Display and Graphics” tab in-game) since the usage of cache will multiply by each client that is run and will thus increase the load on the computer. This applies both when you use premium graphics content and classic graphics content.
Please note that to play EVE with two clients you will need two separate accounts; it is not possible to be online with two separate sessions on the same account.
It's certainly worth a try, right?