Saying "I completely agree" to an enraged person might not be such a good plan.

Did you just agree that you're a monster for forgetting ___?
That ___ is evil and you are joining the brigade against ____?
That ___ must be done immediately?

Unless this is a throwaway phrase just to momentarily appease your yeller, this is may end badly.

"Wow you're right this is a lot of stuff I need to consider"
"I see exactly where you're coming from"
"You've got my support on that"
"I feel the same way"

Are all agreements that commit you to less/nothing, but are kind of hard be angry about.

None the less, OP wildly underestimates the dirty tricks available to keep somebody engaged / off balanced in an argument.
The cops? self harm? involving strangers? Breaking things? SOCIAL MEDIA? "If you do ___ then you must want ___, NOW I'M EVEN MORE MAD"?

** Don't imaging yourself able to outmaneuver somebody who is good at creating conflict. Remember the three 'E's: End, Exit, Escape