The no-stacking rule is on PHB 204. "The effects of different spells add together while the durations of those spells overlap. The effects of the same spell cast multiple times don't combine, however. Instead, the most potent effect--such as the highest bonus--from those castings applies while their durations overlap."
So if you have Aid on you already, the only way to get more Aid is to cast it at higher level.
Just an FYI, I don't pre-buff aid. The strategy I'm considering in a specific instance when a ranged heal is required is to use aid as the ranged heal to get someone back on their feet. The advantage being you get a similar effect to healing word and you get to buff two other party members with five extra hit points. So you cast the aid during the battle as a ranged heal with an additional bolstering effect. This is a highly effective low level AoE Heal option that allows you to preserve spell slots. You should only need a ranged heal in a tough fight. If the fight is already tough, you're getting a really great effect from aid not only getting the fallen player back on his feet, but bolstering your allies.
My caster strategy is always to preserve spell slots. Not pre-buffing aid allows me to use aid for a dual purpose ranged heal and party buff.
As far as the rule debate, this is how we play it. It is only useful when the PC is at zero hit points. As usual, your table, your rules.
I've read that. There is no combining. One replaces the other. You've already lost the five hit points. The new hit points will be the highest bonus. We're talking about a situation where a ranged heal or heal-like effect would be required. Aid serves that purpose for a zero hit point individual that has already lost the extra five hit points from the previous aid.
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