In EBTs the Buddha is recorded to say that i) he taught the Dhamma by the middle, and ii) the path to end of suffering the fourth noble truth is all about is a middle path itself.
In dependent origination-focused suttas like SN12.15, SN12.36, SN12.47 etc the Buddha is recorded as saying that Dhamma he taught was preached by middle due to the formulation of dependent origination. By pointing a model in which experience of suffering through lifetime takes place without a self and in a dependent originated fashion, he was teaching between the extremes of nihilism and eternalism. The usual Pali for that is:
Ete te, bhikkhu, ubho ante anupagamma majjhena tathāgato dhammaṃ deseti
In suttas like MN139 and the famous SN56.11, the Buddha is recorded as saying that it the path he awakened to (abhisambuddhā) taught was a middle way in the sense of avoiding both the extremes of the pursuit of sensual pleasures and the pursuit of self-mortification. The usual Pali for that is:
Ete te, bhikkhu, ubho ante anupagamma majjhimā paṭipadā tathāgatena abhisambuddhā
In the AN3.156, the Buddha is recorded equating the middle way with the 37 qualities conducive or related to awakening (aka 37 bodhipakkhiyādhammā): 4 establishments of mindfulness, 4 right exertions, 4 bases of power, 5spiritual faculties, 5 spiritual powers, 7 factors or limbs of awakening and the 8 noble path factors.
Are there other uses/occurrences of both terms majjhima and majjhena associated to other elements of the Dhamma?