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Wiktionary
max out

vb. 1 (context intransitive English) To reach the limit of one's capability. 2 (context intransitive English) To reach a maximum or a point at which no more growth or improvement is possible. 3 (context transitive English) To use (something) to the limit of its capabilities

WordNet
max out

v. reach a maximum; "I maxed out on all my credit cards"

Usage examples of "max out".

On raising from there Kelly placed Max on a watch in three, assigning him to Kelly's own watch, which gave Max much more sleep, afforded him as much instruction (since the watch with Simes was worthless, instruction-wise), and kept Max out of Simes' way, to his enormous relief.

Ukiah's open honesty moved Max out of his grief-stricken depression to the land of the living.

He's afraid of what will happen if we try to force Max out of the train.

He did glance over as he sat down and moved plastic lunch dishes aside to lean over his arms on the table, Max out of Renee's line of sight if she happened to look this way.

So Chewbaeca, who was closest, slung his bow-caster, took Max out of his eraplacement, and held the computer up to the chutes control panel.

I understand these guys wanted to max out PLS points, which they did, but they might have violated peacetime safety-of-flight rules by taking a broke bird into the air.