Here's a study that shows which proteins active GHBP(and thus potentially which proteins we can manipulate):
The Extracellular Domain of the Growth Hormone Receptor Interacts with Coactivator Activator to Promote Cell Proliferation
So increase levels of CoAA to grow taller.
According to the study "The Coactivator activator CoAA regulates PEA3 group member transcriptional activity.": "Five CoAA interactors have been identified previously: the coactivator TRBP and the histone acetyltransferase CBP, the proto-oncogene coactivator SYT, the extracellular domain of the GH (growth hormone) receptor called GHBP (GH-binding protein), and the transcription factor RUNX2"<-So a likely way to manipulate CoAA is via RUNX2. Diosgenin increases RUNX2 levels. Parathyroid Hormone inhibits Zfp521 which allows for higher RUNX2.
Unfortunately it seems more likely that CoAA stimulates Runx2 than the other way around:
So CoAA stimulates osteoblasts as well as chondrocytes. Unfortunately, no way of increasing serum levels of the CoAA protein is known(which would stimulate GHBP).