Hay was unbeaten on 13 at the end of the T20 final against Old Boys Collegians on Sunday as his side chased down 104 with six overs to spare.
The T20 title adds to the one-day and two-day titles the club won last year, meaning Burnside currently hold all three premier trophies.
Hay said there was a good chance his side could claim all three trophies again this season.
“It’s definitely feasible. It will just come down to us continuing to work hard,” he said.
“If we continue to do that and take games as they come, prepare well for every game, train hard and the guys are enjoying themselves, I don’t see any reason why we can’t keep winning.”
Burnside beat Sydenham by 48 runs in their semi-final to set up the clash with Old Boys, who had earlier beaten Riccarton off the last ball in the other semi-final – Kyle Stevens hitting a four with just one run needed.
The majority of Canterbury rep players were available for the finals with Mitch Hay and Scott Janett playing for Burnside – the latter scored half-centuries in both playoff games – while Matt Boyle turned out for Old Boys and scored 42 in the final.
Opener Oscar Jackson also made the dash from Wellington to play.
After featuring for Onslow in the Ewen Chatfield Trophy competition on Saturday, on Sunday he suited up for Burnside, who he plays for while studying at Canterbury University.
“They’re great lads to have in the team environment,” Matt Hay said.
The one-day competition starts this weekend with a replay of last year’s final between Burnside and Lancaster Park, while Riccarton plays East Shirley, Heathcote host Sydenham and Old Boys visit St Albans.