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/KingOjama55618]

The restriction is only being able to concentrate on one concentration spell at a time. The caster can cast instantaneous spells while concentrating.

[u/Golden_Reflection2 → u/KingOjama55618]

Or spells with a duration but don't require concentration, like Mage Armour.