pessimus, maximus, optimus

What were the phonetical shifts the worked in development of Latin superlatives maximus, pessimus, optimus?

pessimus< *ped-temos cf. peior < *ped-yo:s
maximus < *magi-semos< *?,  cf. maior < *mag-yo:s

Why note *mactimus, if suffix was -temos? this suffix -semo- was < *-t-temo- ?
maximus < *magissemus < *mag-ist-temo- ?
pessimus (alternatively) < *pedissemos < *ped-ist-temo- ?

And how about minor and minimus?
minor < *min-(w)-o:s, *min-yo:s ?
minimus < *min-emo-? *minu-mo- ? (cf. summus < *sup-mos)

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