Simon Katich, Karl Brown and Ashwell Prince all made half-centuries as Lancashire closed on 356-5 against Kent at Emirates Old Trafford.
Kent dropped four catches and just three wickets fell all day as the hosts assumed control.
Katich ended the day 93 not out after sharing an unbeaten sixth-wicket stand of 138 with Steven Croft, who is 47 not out. And in doing so, the former Australian Test batsman passed 20,000 first-class runs.
With national selector Geoff Miller watching on, James Anderson staked a claim to win back his job as nightwatchman for England from Steve Finn by playing his part in a 62-run stand with Brown in the morning session.
The England bowler brought up their 50 partnership with a straight drive for four off Mark Davies but he eventually fell for 26 when he was trapped lbw by Charlie Shreck just 11 short of his highest first-class score.
Brown, who has not scored a first-class century since April 2011, could not fully capitalise, on his 'life', as he was bowled after shouldering arms to a delivery from Shreck on 87, bringing to an end his 93-run stand with Prince.
The South African made his second successive half-century but he too failed to convert when he was given out lbw to Stevens for 58 - although he looked far from happy with the decision.
Katich and Croft upped the run-rate in the final session as Lancashire looked to build a big enough lead to force a result during day four.
And just after Katich had reached his fifty off 77 balls, Mike Powell spurned a chance to get rid of him as he failed to hang on to a skied shot off Tredwell.