Histone demethylases are epigenetic modulators that play key roles in regulating gene expression related to many critical cellular functions and are emerging as promising therapeutic targets in a number of tumor types. We previously identified histone demethylase family members as overexpressed in the pediatric sarcoma, rhabdomyosarcoma. Here we show high sensitivity of rhabdomyosarcoma cells to a pan-histone demethylase inhibitor, JIB-04 and identify a key role for the histone demethylase KDM4B in rhabdomyosarcoma cell growth through an RNAi-screening approach. Decreasing KDM4B levels affected cell cycle progression and transcription of G1/S and G2/M checkpoint genes including CDK6 and CCNA2, which are bound by KDM4B in their promoter regions. However, after sustained knockdown of KDM4B, rhabdomyosarcoma cell growth recovered. We show that this can be attributed to acquired molecular compensation via recruitment of KDM4A to the promoter regions of CDK6 and CCNA2 that are otherwise bound by KDM4B. Furthermore, upfront silencing of both KDM4B and KDM4A led to RMS cell apoptosis, not seen by reducing either alone. To circumvent compensation and elicit stronger therapeutic responses, our study supports targeting histone demethylase sub-family proteins through selective poly-pharmacology as a therapeutic approach.