Harry Brook scored his second Vitality County Championship century of the season and Joe Root his first, while Ben Duckett made 218 as round four continued on Saturday.
Brook (126no off 135 balls) and Root (119 off 190) shared a fourth-wicket stand of 201 for Yorkshire against Derbyshire at Headingley before the hosts declared on 450-5 shortly after lunch on day two.
Brook - who struck a 69-ball ton against Leicestershire during round two - looks certain to be named in England's provisional 15-man T20 World Cup squad which is due to be announced next week.
Duckett is also hoping to head to the Caribbean for the tournament in June and showed his class, albeit in the red-ball format, with a double century for Nottinghamshire at Warwickshire.
Test opener Duckett would offer England a left-handed option in the top six should he go to the T20 World Cup with Ben Stokes making himself unavailable for selection and Dawid Malan, a former No 1-ranked batter in the T20I format, falling out of favour.
England's likely top six - Jos Buttler, Phil Salt, Will Jacks, Jonny Bairstow, Brook and Liam Livingstone - are all right-handed, although Sam Curran and Moeen Ali could be moved up the order if captain Buttler and coach Matthew Mott want a left-hander.
Speaking to the PA news agency earlier this week, Duckett said: "The beauty of what I do is different to a lot of guys. That aspect of not necessarily having the power, but I can use my skills to find ways to get on top.
"I'm 29 now and I'm not going to try to be someone I'm not just to try to get into a side. I've worked out over the years if I become the best version of myself, that's all I can be."
Root appears highly unlikely to make England's squad having played the most recent of his 32 T20 internationals back in 2019, with his next international action set to be in the three-Test series at home to West Indies, which begins at Lord's on Wednesday July 10.
Reigning champions Surrey - second in the early 2024 table - are in control against Hampshire at The Kia Oval.
Watch the County Championship round five match between Lancashire and Kent at Emirates Old Trafford live on SportNews Cricket and SportNews Mix from 10.50am on Friday.
Rory Burns' 25th first-class century - but first since July 2022 - and Jordan Clark's 106 not out from 102 balls helped the hosts to 359 all out before Hampshire closed on 31-2 and trailing by 177.
Current Division One leaders Essex are 314-3 against Durham, and 44 runs behind, after 107 for Feroze Khushi and and an unbeaten 94 Nick Browne.
