Depends on the motive you posit, for one thing. Are you suggesting a firm would reduce prices to raise market share in order to raise profits, either near term or over time (which in either case has enhanced profits as its goal)? Or is market share the goal--because managers prefer the social advantages of a bigger corp.--even at lower profits?
And where does the extra output to serve the larger market come from? Fixed capital (investment) is by definition fixed in the short run. Do they have to hire more (productive) labor, or go to the whip (e.g., "speed-up")? No change in labor, no change in surplus value (depending on the effect of lower prices and more Q on the PxQ calculation that approximates total value). Adding labor to serve a larger market could cut into total surplus value/advanced capital, depending how the numbers worked out (e.g., PxQ).
All in all, an exceedingly minute point, Max. I suppose you could find a corp. that aggressively pursues price cutting to get market share that requires more labor and cuts into surplus value and maybe profits too. And, btw, they could maintain profits by replacing their cronies in the management layers with productiove workers who enhance output. But don't hold your breath. And where are these aggressive, price cutting corps anyway? Nowadays corps get market share mainly by buying it (mergers and acquisitions).
The recent deregulation of electric utilities is a case in point. Dereg proponents argued that "competition" would drive down retail prices. But utilities' predictable response has been a massive merger movement, so they can control supply and prevent that from happening. Once the bubble of exhorbitant nuke costs has been collected during the transition to full dereg (leading to an initial price reduction), you can bet your last dollar some combination of higher prices and supply shortages will quickly become the norm.
RO