Roosters cubmates Roger Tuivasa-Sheck, Shaun Kenny-Dowall and Sam Moa have also joined the squad, along with Melbourne Storm players Jesse Bromwich, Tohu Harris and Kevin Proctor.
This week's additions bring the number of Kiwis candidates to 31, with several more involved in Sunday's NRL Grand Final between Brisbane Broncos and North Queensland Cowboys.
Meanwhile, five-eighth Kieran Foran has withdrawn from the squad, opting for off-season rehabilitation of an elbow injury that has troubled him for much of the season.
The touring squad of 23 players will be named on Thursday, October 8.
Kiwis train-on squad: Gerard Beale (Cronulla Sharks), Jesse Bromwich (Melbourne Storm), Lewis Brown (Penrith Panthers), Manaia Cherrington (Wests Tigers), Greg Eastwood (Canterbury Bulldogs), Sosaia Feki (Cronulla Sharks), Bryson Goodwin (South Sydney Rabbitohs), Tohu Harris (Melbourne Storm), Peta Hiku (Manly Sea Eagles), Solomone Kata (NZ Warriors), Shaun Kenny-Dowell (Sydney Roosters), Isaac Liu (Sydney Roosters), Tuimoala Lolohea (NZ Warriors), Issac Luke (South Sydney Rabbitohs), Simon Mannering (NZ Warriors), Te Maire Martin (Wests Tigers), Ben Matulino (NZ Warriors), Manu Ma'u (Parramatta Eels), Sam McKendry (Penrith Panthers), Matt McKilwrick (Sydney Roosters), Sam Moa (Sydney Roosters), Jason Nightingale (St George Dragons), Kevin Proctor (Melbourne Storm), Curtis Rona (Canterbury Bulldogs), Tim Simona (Wests Tigers), Sio Siua Taukeiaho (Sydney Roosters), Martin Taupau (Wests Tigers), Elijah Taylor (Penrith Panthers), Bodene Thompson (NZ Warriors), Roger Tuivasa-Sheck (Sydney Roosters), Dean Whare (Penrith Panthers).