He already sat in the highest seat. He'd never lower himself to anything below that. To my knowledge, no former-president has ever taken a lower seat in government. Many still find seats of power, but outside the government, I think.
I thought of the limited series with Paul Giamatti on HBO when I hesitated on whether anyone had taken a lower office after being the pres. Not knowledgeable enough to say for sure when I posted. Insomnia now, so I'll keep this in mind for when I'm learning more. Thanks!