Daniel M. Ingram:

Compound jhanas, a term coined by Kenneth Folk, are somewhat artificially created versions of the basic jhanas, where the practitioner, thought the development of concentration and an idea of what one wants to experience, decided to manufacture an experience that is not a standard jhana, but is a hybrid of various factors and qualities.

As concentration becomes more powerful, the mind and experience become more malleable, such that a very wide range of experiences can be constructed to fit with what one is looking for. While one could argue that compound jhanas are a way of paying attention to the sub-jhanas so that one makes them stronger, really there are experiences that one can get into that are not straightforwardly one jhana or another, and really some fusion of hybrid of two or more jhanic qualities, sometimes with specific twists and aspects thrown it for fun and/or interest.

Thus, one might decide, "You know, it would be great to have a jhana that had the panoramic width of attention of Equanimity, but the rich bodily bliss of the second jhana, with just a hint of the spaciousness of boundless space thrown in to make it a bit more relaxing," and, with sufficient concentration and inclination, one can make that happen.

Similarly one might decide, "Those Heaven Realms I have heard described always sounded fun. I wonder if I could make one up. I would like a realm of white light with golden sparkles all over that has the cool, bodily bliss feel of the third jhana," and similarly, with sufficient inclination and concentration, that may show up.

These experiences are clearly jhanic, but mapping them is not easy, as they are compounded out of specific qualities of various jhanas rather than something that is likely to arise through practice that allows the jhanas to progress and develop as they tend to naturally and without this sort of focused and intentional manipulation.