Is there any way to use a display resolution higher than the max?

You could use a virtual desktop; this would allow you to scroll around to support more virtual resolution. But apart from that, no. Your LCD has a maximum resolution. By definition, that means it cannot support a higher resolution.

Many monitors support many resolutions. If your monitor is capable of doing that resolution, then you might be able to get it to scale up a bit. But as far as exceeding a maximum resolution, the answer is usually no. The hardware generally lacks the ability to sync to a resolution that is not supported.

"It sounds like you have a widescreen monitor, given that aspect ratio. 1024x768 is an old school 4:3 resolution (give or take).

Desktop scaling is annoying and will never look quite right.

The BEST thing to do is to buy a new LCD (most new LCDs are widescreen), 19"" and above. Almost all should have a resolution larger than 1024x768.

The most cost effective solution (especially if your PC supports multiple monitors) is to buy a used 17"" or 15"" fullscreen 4:3 ratio LCD - those will do the resolution you need, and it would be neat to have a second monitor on your system. A used 15"" LCD is dirt cheap nowadays."

"If you are looking for an possibility to show simply more Programs virtual desktop_s_ are the solution.

For Windows XP there is a PowerToy allowing different Desktops which could be populated with different Program Windows. I would be surprised if there is no solution for other windows versions. In Linux this is pretty standard. You could switch between the Desktops by an hotkey which is pretty convenient. I would say this is the best solution i know about."

"I would suggest you look for an 'upgrade' to that particular program, or an alternate program that does the same thing at the resolution of any monitor. Virtual desktop solutions eat up your resources and slow down your machine, and there's also a possibility of incompatibility with other software.
The best solution would be to get a second monitor -- an old 4:3 at that lower res should be about $10. If you don't have a dual-monitor capable video card, then you're using something pretty antiquated and you should invest in a newer video card. That will improve your system's overall performance graphics-wise, which essentially means system-wise because Windows is a GUI environment and there's a lot of focus by the system on the graphics involved in displaying Windows, moving them around, etc. Therefore, even if you decide to stay with the multi-res, virtual desktop solution, you'll have improved performance. Your games will perform better also -- always a plus!"