1. There's no such thing as "MNE" - the "never exceed" and "normal operating" concepts behind VNE and VNO apply only to aircraft where Mach effects are not explicitly listed in defining speeds (even though good engineering should account for Mach beffects, the resulting limitations strictly shouldn't be expressed as Mach number limits)
2. VMO is not MMO. Rather VMO and MMO are just ways of saying "the maximum operating limit where airspeed effects dominate" andn "the maximum operating limit where Mach effects dominate" - taken together they JOINTLY define the maximum operating speed limit.
3. 757 and 767, being Part 25 aircraft, do not have VNE defined; VNE is a Part 23 concept. Even if you somehow tried to certify a 757 as a Part 23 aircraft (!) 23.1505(c) would mean that it STILL had a VMO/MMO and VD/MD, not a VNE.
However....
Part 23, per 23.1505, uses both VNE and VMO/MMO nomenclature - depending on whether the aircraft are "turbine airplanes or to airplanes for which a design diving speed V D /M Dis established under §23.335(b)(4)" or not. Therefore, one can attempt to crudely relate the terms.
Assuming that you have defined the structural design speeds VC and VD for your aircraft.
If you now follow 23.1505(a) and (b) you get:
VNE=max(0.9VD or 0.9 max speed demonstrated per 23.251)
and
VNO=max(0.89VNE or VC)
If you follow 23.1505(c) instead you get:
VMO =max (VC, safe margin to VD)
where the safe margin is determined by various speed/gust upset/recovery tests.
In practice, what usually happens is that both VNO and VMO end up being equal to VC. So that would imply that
VNE=1.1(VNO,VMO)
and
VD=1.1VNE
So if your VMO/VNE were 300kts, say, that would imply a VNE of the order of 330-340kts and a VD of about 370-380kts. Basically, VNE ends up being about half way between VMO and VD. Part 25 has such a speed for certification - it's called VFC, and is the maximum speed for demonstration of "flight characteristics". But this is all based on somewhat abusing the certification speed definitions (many of the relations are not "equals" but "not more than" or "not less than" so there's no real way to reverse engineer the speeds for a real case.
Note also that even for aircraft where VNE is the certified speed used, the rules state:
§ 23.1505 Airspeed limitations.
(a) The never-exceed speed VNE must be established so that it is—
(1) Not less than 0.9 times the minimum value of V Dallowed under §23.335; and
(2) Not more than the lesser of—
(i) 0.9 V Destablished under §23.335; or
(ii) 0.9 times the maximum speed shown under §23.251.
23.251 is a FLIGHT TEST DEMONSTRATION. Therefore any aircraft with a posted VNE MUST have been flown at least 10% faster during flight test. Doesn't sound like VNE is a speed where the aircraft is going to be falling out of the sky, does it?