I was thinking Martin Pipe must surely have done this at some point, and Commercial Flyer fits the bill. He won four hurdles races between 12 April and 22 April 2005.
That was in the year the fight for the trainer’s title between Pipe and Nicholls got a bit too heated. Commercial Flyer also won on 26 March, and finished fifth when turned out for a third day in a row on 23 April.