In continuation of our perusal of the studies on transverse momentum spectra for the main varieties of secondaries from a consistent and comprehensive phenomenological approach, we propose to take up here -after a successful completion of reporting in detail the results (Ref. [4] in the text) on our analyses of the p T -spectra of pions -the studies specially on production of kaons, protons and antiprotons in several proton-induced and nucleus-involved collisions at high energies.The measured data on inclusive cross sections of kaons, protons and antiprotons from the various published sources have here been assorted first. Next, data on the p T -spectra of the specific secondaries produced in P P and PP reactions have been scanned and analyzed with the help of Hagedorn's model(HM). Thereafter a connector, named here the combinational approach(CA), hasbeen constructed and used to analyze the data on p T -spectra of some major category of non-pion secondaries produced in nucleus-nucleus(AA/AB) collisions at high energies. And these exercises have, finally, led to the modestly successful interpretations of a wide band of data with the revelation of some insightful physical aspects of high energy interactions. The limitations of the approach have also been precisely pointed out in the end.PACS numbers: 25.75.-q, 13.60.Hb.