Many people look to chemical methods in terms of increasing height. LSJL is in many ways a chemical method increasing the hydrostatic pressure(thus increasing the amount of water, a chemical, per square inch). Hydrostatic Pressure has been shown to induce chondrogenic differentiation. Hydrostatic pressure has been shown to induce chondrogenic differentiation in Type I Collagen(bone). No other substances were used, however, a hydrostatic pressure of 1 MPa was used. The peak pressure observed in the LSJL rat studies was about 0.0013 MPa. Now there are already other chemicals present in the body that encourage chondrogenic differentiation like IGF-1. The more chondrogenic the medium, the lower the threshold of hydrostatic pressure required and the more likely to grow taller.
By supplementing we can recreate the medium in the bone marrow in which scientists have had success in inducing chondrogenic differentiation. Since we don't directly have access to TGF-Beta1, IGF-1, and BMP-2, we have to find ways to indirectly increase them. Since we can't directly inject them, their anabolic effects will occur at a systematic level. So, if you're Justin Bieber, and don't want a deeper voice don't take anything. If you want to be tall but not bigger otherwise then don't take anything.
Dexamethasone can induce chondrogenic differentiation but it also decreases cellular proliferation. It may or may not have permanent affects on height but for now we'll avoid it.
Melatonin indirectly increases TGF-Beta1 but there's an enzyme that is upregulated in response to exogenous Melatonin so it is necessary to cycle Melatonin. Both TGF-Beta and BMP-2 are helpful for early induction of chondrogenesis. However, during active growth plates TGF-Beta is preferable to BMP-2 as BMP-2 encourages mineralization.
Cnidium can increase BMP-2 levels as well as IGF-1 levels. Horny goat weed increases both TGF-Beta and BMP-2. IGF-1 has been shown to increase chondrocyte differentiation levels.
Hyaluronic Acid has been shown to enhance development into a chondrogenic lineage. And High Molecular Weight Hyaluronic Acid has been shown to increase serum levels of HA(divided among all the body tissues of course). Chondroitin has been shown to help stem cell proliferation but I have not directly found something stated it's influence in stem cell differentiation into chondrocytes.
Myostatin has been to shown to inhibit chondrocyte differentiation. So that means creatine can help you grow taller as it inhibits myostatin. Testosterone boosters lower myostatin as well so they can help you grow taller too.
FGF-2 also helps induce chondrogenic differentiation. I don't know of any supplements that can increase FGF-2 levels however.
It's hard to gauge the safety and efficacy of all the supplements. How much of a chondrogenic medium is needed in conjunction with LSJL to induce chondrogenic differentiation? Observe all supplement instructions. Also, when you add a new supplement ask yourself if you notice any new phenotype differences. If you notice differences after supplementation that means that the supplement is likely proving to be effective in making a more chondrogenic medium in your bone marrow. Although we cannot say for sure whether the converse is true, in that even if you don't notice any changes in phenotype it can still be helping make a more chondrogenic medium in your bone marrow.