At tea on day three, MCC are 210-7 in their second innings, a lead of 59, as Yorkshire continue to dominate events.
The champions are chasing a three-day finish - and the prospect of a day off before they return to England on Thursday - after another dominant display.
They captured five wickets in the afternoon session, to go with the two they claimed in the morning, which included the scalp of Alastair Cook.
The England Test captain was caught at mid-wicket by Adil Rashid off Jack Brooks for five, having managed only three in the first innings.
It was a poor stroke by the left-hander, who is desperately seeking form and confidence ahead of next month’s Test series in West Indies.
Cook - England’s leading Test century-maker - has not scored a Test hundred for 22 months, when he hit 130 against New Zealand at Headingley.
Cook caused a stir last week when he described England’s decision to replace him as their World Cup captain as “probably wrong”, in hindsight.
The opener continued his poor form in a one-day international series in Sri Lanka late last year, and England responded by dropping him in favour of Eoin Morgan.
They went on, however, to make an embarrassing early exit from the global tournament in Australia and New Zealand - beating only minnows Scotland and Afghanistan, and eliminated by a defeat against Bangladesh.
Cook agreed to play for MCC against Yorkshire at the Sheikh Zayed Stadium, in the traditional curtain-raiser for the new season.
But there has been no return to form for England’s most prolific Test centurion.
The other wicket to fall before lunch was that of Michael Carberry, caught at slip by Tim Bresna off Adam Lyth for 23.
MCC reached 125-2 early in the afternoon, a deficit of 26, before their innings hit the buffers.
Nick Compton, having played well for 74, was caught behind off Will Rhodes’s second ball, having faced 139 deliveries and hit six fours.
Rashid had Daryl Mitchell lbw for nine and MCC fell to 176-5 when Zafar Ansari played on to Brooks for 15.
Rashid claimed another wicket when James Hildreth went lbw for 49, and the seventh wicket went down right on the stroke of tea when Steve Patterson trapped Chris Rushworth for six.
At the break, Sam Billings is unbeaten on 23 and Adam Riley has yet to score.