Wiktionary
gotten off on
vb. (past participle of get off on English)
Usage examples of "gotten off on".
That was just as well, otherwise the two animals might have gotten off on the wrong foot in their relationship.
He had, she realized, gotten off on an altogether different topic.
You two seem to have gotten off on the wrong foot, and if you continue to let her push you away it can only get worse.
But I kept seeing the way he looked when he hit that woman, and I knew he'd gotten off on it.
After all, she was new to the neighborhood, and she had already gotten off on the wrong foot with this guy.