Recently, non-covalent reactions have emerged as approaches to improve the physicochemical properties of active pharmaceutical ingredients (API), including antibiotics and non-steroidal anti-inflammatory drugs (NSAIDs). This review aimed to present and discuss the non-covalent reaction products of antibiotics, including salt and neutral multi-component solid forms, by framing their substituents and molar ratios, manufacturing techniques, characterization methods, benefits, potency changes, and toxicity, and is completed with an analysis of the development of computational models used in this field. Based on the data, NSAIDs are the most-developed drugs in multi-component system preparations, followed by antibiotics, i.e., antituberculosis and fluoroquinolones. They have reacted with inorganic elements, excipients, nutraceuticals, natural products, and other drugs. However, in terms of treatments for common infections, fluoroquinolones are more frequently used. Generally, NSAIDs are acquired on an over-the-counter basis, causing inappropriate medication. In addition, the pKa differences between the two groups of medicine offer the potential for them to react non-covalently. Hence, this review highlights fluoroquinolone–NSAID multi-component solid systems, which offer some benefits. These systems can increase patient compliance and promote the appropriate monitoring of drug usage; the dual drug multi-component solids have been proven to improve the physicochemical properties of one or both components, especially in terms of solubility and stability. In addition, some reports show an enhancement of the antibiotic activity of the products. However, it is important to consider the possibility of activity changes, interaction, and toxicity when using drug combinations. Hence, these aspects also are discussed in this review. Finally, we present computational modeling, which has been utilized broadly to support multi-component system designs, including coformer screening, preparation methods, and structural modeling, as well as to predict physicochemical properties, potency, and toxicity. This integrated review is expected to be useful for further antibiotic–NSAID multi-component system development.