"We know that ABL works as an epigenetic ‘reader’ of histone and non-histone acetylation.  In doing so, it knocks BET proteins off acetylated proteins and prevents the upregulation of genes associated with inflammatory and oncogenic processes."

BET proteins are the "readers," not apabetalone. BET bromodomains (BD) bind to acetylated lysines on histones to effect gene transcription. Apabetalone binds to the BET BDs (more selective to BD2 than BD1) to compete with BD binding to acetylated lysines. I'm not sure if BET BDs bind to acetyl-lysines on proteins other than histones. They probably do. Nature is complex like that. I kind of think BKC has posted on this before. If he's reading, maybe he can chime in.

"This article https://www.mdpi.com/2305-6320/6/1/24 indicates that ABL’s parent molecule (resveratrol) has other epigenetic capabilities, including activating both writers (acetylation and methylation enzymes) and erasers (de-acetylation and de-methylation enzymes)."   

I'm not an expert in small molecule drug discovery, but the chemical structures of resveratrol and apabetalone look very different. I would caution against assuming too much overlap between resveratrol and apabetalone for target proteins and pathways.

"Has there been any suggestion that ABL possesses epigenetic potential beyond BET inhibition?"

Not to my knowledge. Keep in mind that there are direct and indirect effects. An example of a direct effect would be those proteins/enzymes that apabetalone directly binds to (i.e. binding BD2 of BET proteins). Indirect effects would be those enzymes and processes altered due to transcriptional changes (mRNA changes) brought about by apabetalone. Could some other epigenetic processes (other than direct BET inhibition) be directly or indirectly effected by apabetalone?  Sure. That's possible. Epigenetics is such a broad term and apabetalone seems to effect a large number of biological processes. So it sure sounds possible. I haven't seen (or at least don't recall) any research on this though.

BearDownAZ