While concentrating on a spell, casting another spell doesn't break your concentration unless the second spell also requires it.

Does concentration break when casting another spell?

Casting a spell to hold it for later in the round. Holding a spell requires concentrating on it and will therefore break concentration of another spell already up.

Can you concentrate on two spells at once?

There are no rules for letting you maintain concentration on two spells at once. There are features that can let you cast a spell without needing it to have concentration, some spells can let you avoid having to maintain concentration to sustain the spell if cast at higher levels (such as Major Image).