Cooling, group finance director Nick Newland and Simon Hunt, managing director of sheetfed arm Stones the Printers, are all understood to have left the group last week.
Their departures follow the appointment of former Polestar group business development director David Holland as deputy chairman at the start of last month.
Holland was appointed by Goodhead chairman John Madjeski following the loss of the BT Phone Book contract to Spanish printer Einsa.
Neither side was able to comment while the necessary procedures to finalise the departures were underway.
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