Version Control for Multi-Client Product

I recently joined fast-growing IT company. We have a popular application that hase undergone several revisions. There is a defined base product. However, two upcoming clients requested modifications that would affect the base product individually such that it would seem to be a customization project. This is not what we want. We want the base product enhanced to meet these and other requirements yet still offer each client only those enhancements relevant to his operation.

We do not want to offer one product to this client and another one to a different client, we lose the definition of a product. The modifications are termed fixes (even though they are not bug resolutions) and are presented as addendums to our base technical specifications one on top of the other, meaning the first requirement is fix 1 and the next is fix 2, even though the second may negate the first.

How do we implement version control? Is there a hard and fast rule on how to keep the base product intact while still catering to each client's distinct requirements?