Hot melt extrusion (HME) has become an essential technology to cope with an increasing number of poorly soluble drug candidates. However, there is only a limited choice of pharmaceutical polymers for obtaining suitable amorphous solid dispersions (ASD). Considerations of miscibility, stability, and biopharmaceutical performance narrow the selection of excipients, and further technical constraints arise from needed pharmaceutical processing. The present work introduces the concept of molecularly targeted interactions of a coformer with a polymer to design a new matrix for HME. Model systems of dimethylaminoethyl methacrylate copolymer, Eudragit E (EE), and bicarboxylic acids were studied, and pronounced molecular interactions were demonstrated by 1H, 13C NMR, FTIR spectroscopy, as well as by different techniques of microscopic imaging. A difference was shown between new formulations exploiting specifically the targeted molecular interactions and a common drug–polymer formulation. More specifically, a modified matrix with malic acid exhibited a technical extrusion advantage over polymer alone, and there was a benefit of improved physical stability revealed for the drug fenofibrate. This model compound displayed greatly enhanced dissolution kinetics from the ASD formulations. It can be concluded that harnessing molecularly designed polymer modifications by coformers has much potential in solid dispersion technology and in particular regarding HME processing.