This study represents the design and synthesis of a new set of hybrid and chimeric derivatives of 4,5-dihydro-4,4-dimethyl-1H-[1,2]dithiolo[3,4-c]quinoline-1-thiones, the structure of which the tricyclic fragment linearly bound or/and condensed with another heterocyclic fragment. Using the PASS Online software, among the previously synthesized and new derivatives of 1,2-dithiolo[3,4-c]quinoline-1-thione we identified 12 substances with pleiotropic activity, including chemoprotective and antitumor activity. All the synthesized derivatives were screened for their inhibitory assessment against a number of kinases. Compounds which exhibited prominent inhibition percentage in cells (>85%) were also examined for their inhibitory efficiency on human kinases via ELISA utilizing sorafenib as a reference standard to estimate their IC50 values. It was revealed that compounds 2a, 2b, 2c, and 2q displayed a significant inhibition JAK3 (IC50 = 0.36 μM, 0.38 μM, 0.41 μM, and 0.46 μM, respectively); moreover, compounds 2a and 2b displayed excellent activities against NPM1-ALK (IC50 = 0.54 μM, 0.25 μM, respectively), against cRAF[Y340D][Y341D], compound 2c showed excellent activity, and compound 2q showed weak activity (IC50 = 0.78 μM, 5.34 μM, respectively) (sorafenib IC50 = 0.78 μM, 0.43 μM, 1.95 μM, respectively). Thus, new promising preferred structures for the creation of drugs for the treatment of cancer and other multifactorial diseases in the future have been found.