This jacquard swatch from my stash is in a structure known as Han Damask.
John Becker, in Pattern and Loom (now sadly out of print and fetching astronomical prices in the used book market), describes this ancient Chinese structure as a monochrome weave in which the ground weave is tabby and the figures are warp-faced 3/1 twill.
If the 3/1 twill is drafted by merely adding tie points to the tabby, the two weaves will work nicely together in jacquard work. The weave works best if it is slightly warp-dominant.
The two weaves can be used in tieups or lift plans for block threadings, and also for network drafting based on a 4-end initial.
Becker has an interesting discussion of the use of heddle rods in weaving Han Damask.