I think that your house rules is going against what concemtration and the 5ed philosophy stand for.
Concentration is the rule by which the number bloating (along with bounded accuracy) of previous edition has been eleminated. With one spell per caster upon which it is possible to concentrate, you make sure that a caster will not become untouchable by adding layers and layers of protections. It also prevents the famous CODZILA of the 3.xed in an elegant matter.
Concentration has an inherent weakness, it can be lost. But it also has a few design flaws.
1) Some spells should not be concentration. Two of these are Hunter's mark and Hex. Both spells should have been class feature but to add injury to the insult, they have been made concentration spells.
2) Quite a few concentration spells also allow a save at the end of a creature's turn. This is one of the worst offender in the concentration mechanic, IMHO. It makes some spell almost useless as it is entirely possible for an enemy to shrug off the effect of a spell before any character had a chance to act. Hold person comes to mind.
3) A few damage over time that use concentration are not only concentration but also use your action to actually inflict damage. Witch bolt is such a spell. As soon as 5th level, the spell is useless as a cantrip will do more damage.
Possible ways to enhance concentration spells.
1) Remove some spells from the concentration mechanics. This is what I did with two of these. So far, it works really well and the two spells are still spells and classes that uses them are not unbalanced in the least. We are currently checking for an other spell to remove from the concentration mechanic but I am not sure that Shield of faith should be one that should be free of concentration.
2)The save at the end of turn. This is a big problem as I wrote earlier. We circumvented this by using the reactivation rule. Reacrivation allows a caster to reactivate the effect of a concentration spell that has been shrugged off by a successful save from a creature. It costs a bonus action to do so and limits a caster to cast only a cantrip when he reactivate an effect. If a creature succede its initial save or a reactivation save the spell ends as normal for this creature. Only one reactivation is allowed.
3) The damage over time effect of some concentration spells should not use your action but a bonus action instead. This one could be quite powerful if allowed with some powerful spells. We concluded that using a bonus action should also count as spell cast with a bonus action. This limits a caster of witch bolt to cantrip casting.
These three modifications are easy to remember, do not change the concentration mechanic much and keeps its philosophy mostly intact.
At four players, keeping track of only one spell per caster is easy. With six players, all of them casters, it starts to be a bit more tedious. Imagine with 12 different spells...
I certainly would not like to return to the spread sheets of 3.xed, it slowed combat way too much, especially after a dispel magic where everything had to be calculated anew.
Your solution is not bad in itself, especially at low levels and with 4 players or less. But as the levels rise, so is the complexity of the game and the tracking of "boosting" spells. At 6 players, it will become tedious much earlier.
If you absolutely need to concentrate on two spells at a time, I would go for
@dnd4vr 's solution. It is simpler and it offers a high risk high reward trade off.