TORONTO — Dynamex’s secret admirer isn’t giving up on trying to acquire the North American same-day delivery and logistics provider without a fight.

Strongly rumored to be to be Canadian trucking giant TransForce, the unnamed company took another shot in the bidding war for Dynamex, which last week announced its board had accepted an increased offer by an affiliate of Greenbriar Equity Group (DashNow) for $24 per share.

That topped a $23.50-per-share offer by the mystery bidder, which has been reported by more than one industry analyst to be TransForce.

The unnamed suitor has now come back with a second offer of $25 per share, or $248 million.

As part of its deal with Greenbriar, Dynamex would have to pay a $7.7-million termination fee if it turned around and went with the superior offer by the unnamed bidder.

However, Dynamex’s board rules also state that failure to accept a "superior offer" would violate the directors’ fiduciary duties to the company’s stockholders.

TransForce, which operates Canpar and a handful of other smaller courier fleets in Canada, is said to be aggressively pursuing Dynamex to leverage its metrics in that sector and pricing pressure.

Dynamex, which reportedly has as much as 40 percent of its revenue in Canada, is currently seen as a major competitor to TransForce.