The Coatbridge boxer was in devastating form as he overwhelmed feisty Englishman Kevin Mitchell to retain his WBO lightweight belt at the SECC on Saturday night.
But Burns, and his wily trainer Billy Nelson, believe that the two-weight world champion will keep improving, and become even stronger.
"There's more to come," insisted Burns, who was previously WBO super-featherweight champion. "The better the guy in front of me, the better I fight.
"I'll fight whoever's put in front of me. Frank Warren (his promoter) knows the fights that I want, I'd love to go after the Ring magazine belt and unify the titles.
"Scott Harrison's itching to get another world title fight, it would be a massive fight in Scotland, but we'll find out more in the next couple of weeks."
Burns' view would make Mitchell wince, since the hard- hitting Dagenham boxer was outfought and could not cope with his rival's aggression or power, with referee Terry O'Connor halting the fight 2 minutes 54 seconds into the fourth round.
Mitchell had twice been knocked down in the round, and he looked stunned by the sheer ferocity of Burns' ring work.
It was a thrilling display by the champion, in the seventh world title contest of his career. He fought on the front foot and more adventurously than he has in the past.
The Englishman hung on for the opening two rounds, but struggled once Burns started landing his booming right-handers.
"He's like an Energiser battery, he doesn't stop the fella," Mitchell said. "He was awesome. He'll mix it at any level of the sport.
"He's getting better and there are no boundaries for him. He's got the strength and staying power.
"I don't think there are any world champions at lightweight out there who will bother him."
Burns recently married, and he will fly out to Las Vegas this week with his wife, Amanda, for a well-earned break.
It is a measure of the cham-pion's commitment and hunger, though, that he will take his training gear with him. He will also try to seek out Floyd Mayweather, the five-division world champion who lives in Vegas.
"I'd love to meet him, and maybe get a couple of rounds of sparring off him," Burns said with a smile.
"I've been out there before, but not for one of the big fight weekends. Fighting in Vegas is definitely something I would like to do.
"But as long as I'm fighting regularly and staying active, that's all I'm interested in."
Burns will get his wish, since Warren intends to arrange another title defence – the Scot's third – on either December 8 or 15.
The venue is yet to be decided, but it will be a big show, with George Groves and Billy-Joe Saunders also on the card.
Warren believes, however, that Burns is not only Britain's most improved fighter, but also the best of the UK's current world champions.
"If he keeps going at this rate, he'll be a champion for a long, long time, and he'll unify titles," Warren said.
"He's just a gentleman, a great advert for boxing and sport. He lives the life. He's not got big-headed, he's just naturally a nice guy.
"He doesn't cut corners, he doesn't cheat and that shows in the ring. He's fearless. It doesn't bother him who he fights either."