xna - How can I handle the combination of multiple shader effects?

To be able to work efficiently with effects, is there a good way to combine multiple reusable "base" effects to achieve a more complex final result?

For example, say I have an effect that handles multi-texturing and one that handles ambient lighting. I'd like to combine them to achieve a final "ambient-lit multi-textured" effect.

This seems troublesome unless effects somehow can share information. When I just use the multi-texturing effect, I get the result I want. But when I afterwards apply the ambient lighting effect to intensify the color some value, it uses just uses the color from the ambient effect.

Is there a way to solve this? So that each effect can be individual and somehow not screw up the other effect? Or do I have to resort to manually writing one large effect file that lacks any flexibility?