In many cases you can with LGPL, and you can with GPL if you explicitly add a licensing exception.

Also, regarding "use ... proprietary modules ... to better your program or library": depends on your definition of "better", but if that's one of your goals, then I agree that you don't want the GPL.

To add onto it in a beneficial way to the user. Also, MPL allows static linking, the LGPL doesn't unless you explicitly state it.

For the record, would 'GPL + Linking exception' be incompatible with the GPL and LGPL?

> Also, MPL allows static linking, the LGPL doesn't unless you explicitly state it.

The LGPL allows static linking, as long as you provide the means to relink with a modified version.

> For the record, would 'GPL + Linking exception' be incompatible with the GPL and LGPL?

Only in one direction. You can take code under the GPL plus a linking exception and merge it into a GPLed project, but the result will not have the exception, so you can't add proprietary code to the result.