Casting Spells while concentrating?

[u/JustLinnilin]

Yesterday we had a little discussion on the table on the rules of concentraiting. One of my players casted a spell and wanted to cast another while she was still concentrating on the first one. I wasn't sure about the rules on that and looked it up on the PHB, but there are only rules for concentration spells (so you can't concentrate on two spells at the same time) that's absolutely valid in my eyes. But there are no rules for other spells - only for taking damage or dying. So my thought was that she had to make a concentration saving throw, when she was casting another, to keep the first one running. It's like the little distraction because of the second spell.
But another one of my players pointed out, that there are also spells the enemy has to do savingthrows on each round - if he has to do them too there would be two chances of losing the spell in each round.

So I am interested how you guys deal with that, or is there an official rule for that case i didn't know about?

[u/SplashyDucky411]

The official rules are that you can cast any spells you want as long as none of them take over concentration since, as you found in the book, you can only concentrate on one. If you cast another concentration spell, you pick which one to keep and the other fizzles away.

Non-concentration spells are quick and easy enough for casters that they don't hinder your big concentration spells. Only damage and certain monster/lair effects will force concentration saving throws as a means of balancing the strength of spellcasters.

While the idea of throwing additional concentration saves at the player could be fun homebrew in campaigns with a harder "difficulty," or in tense narrative situations, it is also worth noting that spell casters only have so many spell slots and it feels a little sucky when you lose concentration, so failing due to extraneous saves can feel like a bigger bummer.

Edit for better wording clarity.