I do like the concentration rules and see the benefit of their implementation in 5e, for similar reasons to those others have stated.
However, I also agree that NPC casters aren’t the threat that I want them to be. It is also too limiting to be unable to cast even one control spell just because you have a defensive spell active. And, since there are casters in my game who also wanted to enjoy more casting flexibility, we agreed that loosening the rules would work well, so I came up with this:
Multiple Spell Concentration
With this house rule in effect, a spellcaster can maintain more than one spell that requires concentration, with the following restrictions:
1. A spellcaster may not have more than one concentration spell active on a single target (or overlapping area) at a time. If he casts a concentration spell targeting a creature (or area) on which he is already maintaining a concentration spell, the previous spell ends.
2. To successfully cast a concentration spell while another concentration spell is active, the caster must succeed a concentration check DC 10 + spell level + 1 for each concentration spell. Failure indicates that all previous concentration spells end.
Example: the DC to cast Haste while already concentrating on Fly and Stoneskin would be 17 (10 + 3 + 2).
3. The total level of all spells maintained through concentration may not exceed twice the caster’s highest level spell slot. If casting a new concentration spell would cause the total levels of maintained spells to exceed this limit, all previous concentration spells end.
E.g. An 8th level wizard’s highest spell level is 4, so he can maintain concentration on up to 8 spell levels. He could maintain two 4th level spells, or four 2nd level spells, etc.
If a spell is cast at a higher level, use that higher level when determining total spell levels maintained.
(Note: this restriction is based on max spell level slot, rather than character level, to avoid confusion and or abuse with multi-classing. "Half-casters", like a paladin, also shouldn't be able to maintain spell levels equivalent to, say, a wizard.)
4. The DC to avoid losing concentration when damaged is increased to 10 + Highest Spell Level + 1 for each spell, or equal to the damage of the attack, whichever is higher.
(Note: It is a harsh DC, and we may adjust it based on experience during play - but I initially thought it a fair trade for the increased power.)