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.
- If A still has its Reaction available, they can cast Counterspell for trying to nullify B's Counterspell. If A has no Reaction available, they can not cast it.
Let's consider the following case:
- (a) A casts 3rd level Fireball.
- (b) B uses their reaction and casts 3rd level Counterspell: in this way, A's Fireball would be successfully counterspelled.
- (c) A has their reaction available: they cast Counterspell vs B's, which is hence nullified by A's, who can keep on casting Fireball with success.
Suppose now that in (b) B casts Counterspell at 4th level and in (c) A casts it at 3rd level: by the rules of the spell, an ability check is required (DC 14, in this case). If A wins, then B's Counterspell is nullified and then A resorts to its Fireball casting, while if A loses B's Counterspell nullifies A's Fireball.
This very scenario is depicted in the latest version of the Sage Advice Compendium:
Can you cast a reaction spell on your turn?
You sure can! Here’s a common way for it to happen: Cornelius the wizard is casting fireball on his turn, and his foe casts counterspell on him. Cornelius also has counterspell prepared, so he uses his reaction to cast it and break his foe’s counterspell before it can stop fireball.
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.
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.