Except, note that the rules for Concentration are based on each hit, not each spell. So things like Magic Missile, Scorching Ray, or Eldritch Blast (at higher levels) will force MULTIPLE dc10 con saves. Making one? plausible. Making three or more in a row? not very likely unless the caster was built specifically for it.
I did not mean this as a specific task to work towards, but as something to keep in mind. You don't want to be using Counterspell on an enemy's Magic Missile, for instance, as that is a completely unfair trade in slots; the goal would be to at least try and make sure you don't expend more resources then they do, if not use less.
As far as counterspelling a counterspell, I don't think you quite understand the action economy here. You say you counterspelled the counterspell of an enemy that was casting a shield, which allowed someone to attack the enemy. This makes no sense, because counterspell is a reaction; either you Counterspell it once, he counter-counterspells you, and continues his spell because you used your reaction (or not, depending on the DM's ruling), or you don't counterspell his shield, and he just casts it. In no way can the action economy allow you to counterspell something twice unless it is during, then just after it, as you get your reaction back at the end of your turn. Now, RAW, it IS technically possible to cast a spell, the enemy counterspells you, and then you use your reaction to counterspell the enemy counterspell against your spell; but as I stated before, it would be ill advised, regardless of DM ruling on the matter, because doing so causes you to use two spell slots for the enemy's one, which is definitely more of a victory in the enemy's part, particularly since most wizard duels involve non-wizards still being the primary targets.