How can an aircraft’s maximum design operating speed be greater than its never-exceed speed? According to this AAIB report on a June 2009 mid-air collision between an RAF Grob Tutor and a glider, the Tutor’s maximum design operating speed (VDO) is greater than its never-exceed speed (VNE):


(5) In the case of aerobatic category aeroplanes, allow each occupant to abandon the aeroplane at any speed between VSO and VDO10;  [Quoting the applicable certification requirements for aircraft emergency exits; footnote in source.]

[...]
10 VDO is the maximum design operating speed which for the Tutor is 1.1 VNE or 205 kt.  [The report’s explanation of the aforementioned footnote.  The bolding is mine.  Everything I have quoted from the report comes from page 62 (numbered as page 52).]

The point of the never-exceed speed is, as indicated by its name, that this speed should never be exceeded in this aircraft for any reason whatsoever; as such, aircraft are generally designed and certified with maximum operating speeds well below VNE.  How can the Tutor’s design maximum operating speed be greater than its never-exceed speed?
Maximum design operating speed means "we calculated the aircraft will break apart at that speed". It's obviously higher than the never-exceed speed, which means "you can safely operate the aircraft up to that speed".

Key here is the word "design". It always means something along the lines of "we calculated it to break at that load, please never try". The quotient of design load and maximum expected/allowed load is called safety factor. In this case, the safety factor is 1.1.