In the pursuit of hydrophilic model fac-[Re(CO)3]+ complexes for (radio) pharmaceutical applications, six novel [2 + 1] mixed-ligand complexes of the general type fac-[Re(CO)3(bid)P] were synthesized and characterized, where bid is a bidentate ligand bearing either (N, O) or (S, S′) donor atom sets and P is the hydrophilic phosphine 1,3,5-triaza-7-phosphoadamantane (PTA) or its macrocyclic homologue 1,4,7-triaza-9-phosphatricyclo[5.3.2.1]tridecane (CAP). The (N, O) ligands used in this study were picolinic and quinaldic acid, while the (S, S′) ligand was diethyldithiocarbamate. The complexes were synthesized in generally high yields and purity and the characterization was performed by spectroscopic methods, IR, NMR, and elemental analysis. Detailed X-ray crystallographic study of molecular packing by using Hirshfeld analysis tools revealed a plethora of intermolecular interactions such as hydrogen bond, π⋯π, C-H⋯π, and carbonyl-carbonyl interactions. To our knowledge, the CAP complexes reported herein are the first example of [2 + 1] mixed-ligand fac-[Re(CO)3]+ complexes with CAP. The new complexes might have the potential to serve as platforms for the design of target-specific complexes with favorable pharmacokinetics.