counter offer
noun

a higher or lower offer made in reply to another offer

Example

Smith Ltd made an offer of $1m for the property, and Blacks replied with a counter-offer of $1.4m.

"...the company set about paring costs and improving the design of its product. It came up with a price cut of 14 per cent, but its counter-offer - for an order that was to have provided 8 per cent of its workload next year - was too late and too expensive" [Wall Street Journal]

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