Muller quickly became a fan favourite in Montreal, and he helped them win the Stanley Cup in 1993. He was traded to the New York Islanders during the 1994–95 NHL season. Initially, he was reluctant to report to the Islanders, then played a handful of games in an uninterested manner before team management decided that his poor attitude outweighed his potential contributions on the ice and barred him from the team. Eventually, the Islanders recalled Muller, but he refused to report, freeing the Islanders from their contractual obligations to pay him. Ultimately, Muller was traded at a discount to the Toronto Maple Leafs, in a three team trade that saw Muller and Don Beaupre go to the Maple Leafs, Martin Straka, Ken Belanger and the rights to Bryan Berard go to the Islanders while Damian Rhodes and the rights to Wade Redden went to the Ottawa Senators. Muller had his last 20 goal season with the Maple Leafs the next season, but he was traded to the Florida Panthers as the Leafs fell out of the playoff picture.