Men's Wearhouse said it offered to acquire all outstanding shares of Jos. A. Bank for $57.50 per share, higher than its November offer of $55.
The tender offer, the latest move in a long battle between the two retailers intent on playing the lead role in creating a combined entity, expires on March 28.
Men's Wearhouse also said it intended to nominate two independent directors to Jos. A. Bank's board.
(Read more: Jos. A Bank rejects Men's Wearhouse bid)