It is interesting that in all of this discussion no-one has mentioned OEI climb gradient! Remember that, essentially, V2 is the minimum speed at which a specified gross climb gradient (OEI) can be achieved (2.4% 2-engined aircraft, 2.7% 3-engined, 3.0% 4-engined). The 1.2 x Vs and 1.1 x Vmca are caps below which V2 cannot go.
A lot of the discussion above can be simplified by saying that Vr cannot be less than Vmcg. When V1 = Vr = Vmcg, V2 is the speed which is achieved at screen height following rotation at the normal rate for the aircraft type.
The case in point here, the B742, does reach this situation at light TOW, although the Boeing take-off data is a little confusing as the shaded part (low TOW) of the T/O speeds table just notes that this area is "minimum control speed limited". As there is no promulgated Vmca-1, this must be a Vmcg limiting case. As has been stated above, what actually happens to V2 will depend on the variation of Vmcg with AUW and the acceleration from Vr to screen height. However, do not try to read too deeply into the B742 table; I have never quite figured out quite what is happening! One thing to be wary of is that if your company SOP is to set the ASI bugs for departure based on V2, they will be set artificially high. In such light TOW cases it is worth calculating the approach Vref for the AUW as this is the true speed on which flap retraction should be based (ie stall margin). Therefore, if you end up with a loss of thrust and high drag after T/O, you are aware of the true min speed for flap retraction should you really need it.
With regard to Vmcg and crosswind, in the B742 you need a speed greater than Vmcg by approximately an extra 1.3KIAS per kt of crosswind in order to maintain control to the same criteria (max 30 ft displacement from centreline, max 150 lbs rudder force). Note that the B742 was originally certificated in the UK to BCARs which assumed a 7 kt crosswind, and some operators may still use these figures. Crosswind is ignored in FAR and JAR 25 on a statistical basis related to the probability levels of losing an engine in an adverse limiting crosswind!!! I agree with the above comment that the best you can do is to use the scheduled V1 for RTOW although knowledge of V1 max (ie Vstop) would help even more. Note also that Vmcg is based on aerodynamic control alone so the NWS will help for real.