Making the Concentration limit a hard 1 in 5E is a missed opportunity.
Wiz could get a familiar/homunculus at lvl 6 that concentrates on one spell while the caster concentrates on another or you could upcast any concentration spell by 3 lvls to make it no longer require concentration or whatever.
Yeah, a hard limit of 1, without ways to expend it is a bit harsh.
Also greatly lowers the value of most Concentration spells - and makes the value of non-Concentration spells skyrocket.
Edit: I still think its a good direction, only some allowances should have been made - a feat and/or subclass (like Desiderius' suggestion) that increases the limit. Maybe even some item that can "hold" an active spell.
I think a top limit of about 3 Concentration spells active could be just about right overall.