Resistance to antibacterial agents is a growing global public health problem that reduces the efficacy of available antibacterial agents, leading to increased patient mortality and morbidity. Unfortunately, only 16 antibacterial drugs have been approved by the FDA in the last 10 years, so it is necessary to develop new agents with novel chemical structures and/or mechanisms of action. In response to this, our group takes up the challenge of designing a new family of pyrimidoisoquinolinquinones displaying antimicrobial activities against multidrug-resistant Gram-positive bacteria. Accordingly, the objective of this study was to establish the necessary structural requirements to obtain compounds with high antibacterial activity, along with the parameters controlling antibacterial activity. To achieve this goal, we designed a family of compounds using different strategies for drug design. Forty structural candidates were synthesized and characterized, and antibacterial assays were carried out against high-priority bacterial pathogens. A variety of structural properties were modified, such as hydrophobicity and chain length of functional groups attached to specific carbon positions of the quinone core. All the synthesized compounds inhibited Gram-positive pathogens in concentrations ranging from 0.5 to 64 µg/mL. Two derivatives exhibited minimum inhibitory concentrations of 64 µg/mL against Klebsiella pneumoniae, while compound 28 demonstrated higher potency against MRSA than vancomycin.