3 wire to 4 wire for new stove
When I hear  neutral called "common" I think someone is likening the Neutral to the concept in electronics of "Common" or "GND" or "Vss".  That is wrong. There is indeed a thing like that, but it is Equipment Safety Ground, and it does not handle current except during fault conditions. 

Other than that, mains electrical is wired effectively as an "isolated system", which each Neutral current return wired very much like it is another hot.  Neutrals are not spiderwebbed.  You cannot return current on any arbitrary neutral.  Mains wiring is very particular which neutral is used to return current for a particular hot.  Why, you ask?  Several reasons to start.   


Not least, Neutrals don't have breakers.  Most siliconheads forget that.  If that stove is returning 10 amps while your microwave is returning 15 amps, it is returning 25A of current on a 15A wire which again, has no breaker.  Whoops! 
Currents must be equal in each cable or conduit. Because this is AC power, and EMFs are a thing.  When currents are unequal, the EMF thrown by the various wires do not cancel each other out, and cause all sorts of mischief, including vibration of the wires, leading to fatigue failire, arcing at the failure point, and heat/fire. 
No Looping. If current went in a loop around something, aside from the above problem, what's inside the loop would become the core of a transformer. Among other things, this causes eddy current heating in anything metallic.  Special considerations must be made even when several wires are put in adjacent conduits due to space limitation reasons. 


The upshot of all this is that mains wiring must be a strict tree topology, no looping or crossovers.  

Grounds are allowed to loop or spiderweb because current does not travel on them except during fault conditions. 

Oh yeah.  You can retrofit ground.

And here is where you are in luck.  The three wires to your old stove connection are not are not hot, hot, ground.   They are hot, hot, neutral. No ground.  

It is completely legal for you to continue in service the H H N conductors,and retrofit a ground.  

However, the ground path needs to be the full thickness required for a ground of a 30/40/50A circuit, which is 10 AWG.   It must be that width all the way back to the same service panel the conductors come out of, you cannot poach the smaller #12 or #14 ground off the nearby plug.  

It will suffice to reach anywhere that has a #10 or larger ground path back to the panel, including grounded 30+ amp appliances such as water heater, A/C, dryer if 4-prong, etc. it will also suffice to reach the grounding electrode system, the bare copper wire from the panel to the grounding rods.