Yes, provided you have a Reaction available.
The Counterspell description says (emphasis mine)
You attempt to interrupt a creature in the process of casting a spell.
If the creature is casting a spell of 3rd level or lower, its spell
fails and has no effect. If it is casting a spell of 4th level or
higher, make an ability check using your spellcasting ability. The DC
equals 10 + the spell's level. On a success, the creature's spell
fails and has no effect.
Under "Casting Time", the PHB (pag 202) says (emphasis mine)
Some spells can be cast as reactions. These spells take a fraction of
a second to bring about and are cast in response to some event.
Hence, the steps are the following:
- Caster A casts a spell.
- While A is doing the magic (moving hands, chanting, et cetera), caster B casts Counterspell. Suppose that B has success.
- Two possible interpretation may arise:
- A can "pause" its casting to use its Reaction (if available) in the middle of casting a spell and cast Counterspell too, to contrast B's. In case of success, A resumes to cast its spell which has normal effect.
- Casting a spell does not allow any "pausing", hence there is no way that A succeeds in casting its spell.
The first interpretation satisfies the description of Reaction casting time: by RAW and moreover under what it is written in the latest version of the Sage Advice (pag 14, Can you cast a reaction spell on your turn?) you can use Counterspell as a response (reaction) to a Counterspell of another caster while you are casting a spell. The second interpretation is in contrast with the first one: hence it is not valid.
Or does this mean that Caster B can cast another counterspell to counter Caster A's counterspell attempt?: No, because B has only 1 reaction per turn that had already been used for casting the first Counterspell.
If there would be a 3rd caster C, then C can cast Counterspell on B's Counterspell, allowing A's Fireball to be activated, without A being forced to use another 3rd (or higher) spell slot.
Under a role-play point of view, we can see the Counterspell as just one (or more) gesture(s) that ruins the manipulation of the Wave by a caster. Using Counterspell against another Counterspell during a spell casting is possible (just add a simple gesture to the casting), and it can be seen as the two casters battling for mastering the Wave.