The system is robust enough to allow for multiple reactions to fire in chain and in response to each other - reacting to reactions does occur in some places; If you run to provoke opportunity, the enemy can react, and you can shield their attack, and the enemy mage nearby can counterspell your shield; this is a chain of reactions that works in the game currently, so I'd be surprised if counterspell chains didn't work just fine.

There was an issue, several patches back, where reactions weren't refreshing properly, and were tying themselves to the round, rather than the individual character's turn, and that was causing problems of not offering counterspell against enemy casters when it should have been available, however, I think they've since fixed that problem. They've also just fixed the issue that popped up of creatures with legendary actions skipping their main turns, so that's nice too ^.^

(Niara's big complaint with the arbitrary BA casting rule in 5e)

On the subject of counterspeell... would you like to know something ridiculous and arbitrary and stupid that the bonus action casting rule creates if it is adhered to?

Scenario 1) Julius the archmage (18 Wiz 2 Fi) steps out onto the battlefield, surveys the scene and targets the enemy casters. He starts with meteor swarm! The enemy mage sees this and desperately tries to counterspell it, but, not recognising the spell other than something big and bad, just use the highest slot they have - a 7th. Julius, master wizard, scoffs at this mid-cast, and handily counterspells their counterspell with an 8th level slot! He finishes casting meteor swarm and rains destruction on the enemy lines. Some survive, including that impudent enemy caster, so Julius decides to action surge, and then casts an 8th level disintegrate at the fool, who - having used their reaction - can do nothing except fail their save and be smote into dust. Good turn, Julius. A perfectly legitimate, by the book, allowable turn, that let Julius spend a 9th, and two 8th level spell slots.

Scenario 2) Julius the archmage (18 Wiz 2 Fi) steps out onto the battlefield, surveys the scene and targets the enemy casters. He taps his staff on the ground as he goes, casting shillelagh on it, just to keep the riff-raff away. The enemy mage sees this and, not sure what he's up to, counterspells it at base level. Julius... Cannot counterspell the enemy mage's counterspell. The rules say he's not allowed to. So, his cantrip is interrupted. Julius still has his action (and his reaction) available... but he cannot cast any proper spells with either of them; as he steps out, an enemy ballista bolt comes his way, but Julius, despite having his reaction available, cannot shield it! Frustrated, Julius takes a breath, centres himself then uses his action surge to have a fresh action to do something with, since his (still unused) original action is apparently tainted. But no... even his fresh action cannot be used to cast any of his useful spells. Plans foiled, Julius dodges with one action and dashes with the other to retreat back out of sight again in shame. Total spells: one cantrip (failed).

The bonus action rule is stupid.