1982 saw Muggleton become as a second rower an integral part of Parramatta's most dominant NRL team, providing a second kicker to support Peter Sterling, who was later to become his brother-in-law, and showing abundant ball skills to create opportunities for a famous backline of Sterling, Brett Kenny, Mick Cronin, Steve Ella and Eric Grothe, Sr. Muggleton was chosen for the 1982 Kangaroo Tour, which became known as “The Invincibles” as it steamrolled through England and France to win all 22 games, the first time the Aussies had gone through a Kangaroo Tour undefeated.

However, after that, Muggleton had a great deal of trouble retaining his place during a succession of injuries and much competition from Mark Laurie, Peter Wynn and Steve Sharp in Parramatta's second row.

By 1984, he was used chiefly as a reserve, and in 1984–85 Muggleton had a spell in the UK playing for Hull FC, alongside Sterling, in the then Rugby League First Division.

After this, Muggleton turned to coaching, being most successful with North Sydney's struggling President's Cup outfit in 1993 where he lifted them from twelfth to sixth.

His last game as the defence coach of the Rebels was a home game against New Zealand franchise the Highlanders, a match that also turned out to be the last Rebels match for head coach Damien Hill and players James O'Connor, Gareth Delve, Cooper Vuna, Ged Robinson, Nick Phipps and Nic Henderson.