Miller continued his good day with an unbeaten 30, along with support from Dave Croucher who was again in good touch with a gritty 40.
Parlane hinted that a declaration early in play may be on the cards as they look to bowl Kamo out for less than the home side's first-innings total, hopefully earning a well-deserved outright victory and maximum points as the two finalist positions heat up.
In other Oxford Trust two-day matches, Onerahi's Henry Cooper again starred. But, this time it was with the ball as the off-spinner (five for 13 off 10) kick-started an avalanche collapse for Boys' High. After earlier denying the in-form Dewayne Bowden, Boys' High pushed on to 59 for one, before losing nine wickets for 31 runs in being bowled out for 90.
Boys' High's Kashmir Harypursat scored a defiant 35 and put on 53 with Sam Clotworthy, but the competition leaders' other batsmen hardly troubled the scorers.
In reply, Brad Kneebone played a determined and well-paced innings for Onerahi as he battled hard and scored an unbeaten 100 off 158 balls, giving his team a lead of 145 before declaring.
Kneebone was primarily supported by Bowden (43) as both Chris Harrison and Todd Behre also formed 50 partnerships in conjunction with Kneebone.
Sent back in to bat, Boys' High then had 19 overs to survive the day's play. The youngsters managed to show some resilience and finished the day at 37 for 3, with Ben Smith being dismissed in the last over.
Boys' High coach Stephen Cunis was under no illusions it would be a huge ask for the boys to bat all day next week to try and save the game, commenting: "We will certainly do all that we can to hang in there but let's face it, some rain would certainly be helpful."
In Kaipara Flats' match against City, City was sent in to bat, making 165 all out. In reply, City then bowled tidily and had the hosts in trouble at 147 for 9 at the day's end.