So Spellcasters have more buffs they can cast that are self only and don't require concentration:
Examples: Armor of Agathys, False Life, Mirror Image
There are also group buffs that don't require concentration
Examples: Jump, Longstrider, Mage Armor, Sanctuary, Aid, Darkvision, Protection from Poison, See Invisibility
As you can see these are minor buffs, and great utility spells, or contingency spells. You can have as many of these running as you like.
Most strong group buffs, and summons require concentration. Which only allow one per caster.
But that's not all- Then you have potion buffs, some of which don't stack!
You can only have one of the below running per character:
Potion of Poison/Lightning/Fire/Cold/Psychic/Force resistance
Potion of Hill Giant Strength.
So if you have a Potion of Fire Resistance and you use a Potion of Hill Giant Strength, you lose the Fire resistance potion.
You can use the below two potions as separate buffs:
Potion of Speed
Potion of Animal Speaking.
So you could have Potion of Hill Giant, Speed and Animal Speaking all running together but could not add Fire resistance or it will overwrite the Potion of Hill giant strength.
Nothing in the descriptions alludes to this conflict.