I know it's a lot to ask, but could you please do it anyway?
Literal
Impossible [object-を] acknowledge [with-で] do humbly-receive give-favor-not [polite-ませんか].
無理を承知で = 'knowing it's unreasonable,' a set phrase prefacing a request the speaker admits is burdensome. 承知する ('to consent, to acknowledge') here in its sense of 'being aware of.' Softens a tough ask.