Epigenetic modifiers acting through polypharmacology mechanisms are promising compounds with which to treat several infectious diseases. Histone deacetylase (HDAC) enzymes, mainly class I, and extra-terminal bromodomains (BET) are involved in viral replication and the host response. In the present study, 10 compounds were designed, assisted by molecular docking, to act against HDAC class I and bromodomain-4 (BRD4). All the compounds were synthesized and characterized by analytical methods. Enzymatic assays were performed using HDAC-1, -4, and -11 and BRD4. Compounds (2–10) inhibited both HDAC class I, mainly HDAC-1 and -2, and reduced BRD4 activity. For HDAC-1, the inhibitory effect ranged from 8 to 95%, and for HDAC-2, these values ranged from 10 to 91%. Compounds (2–10) decreased the BRD4 activity by up to 25%. The multi-target effects of these compounds show desirable properties that could help to combat viral infections by acting through epigenetic mechanisms.