Yes and no
A creature can be "affected" by spells that are running simultaneously/co-currently, but the effects do not stack.
For instance, two separate clerics cast Bless on the same creature, it gets the following benefit:
Whenever a target makes an attack roll or a saving throw before the spell ends, the target can roll a d4 and add the number rolled to the attack roll or saving throw.
The benefits do not stack but, if one cleric loses concentration, the other spell would still remain active and the creature would continue to benefit from a d4 bonus to their attack rolls and saving throws until the end of the spell, or until the second cleric loses concentration.
This would be the same for other similar spells, such as Guidance or Resistance.
The same is true for spells that cause detrimental effects, for instance with Bane. In this case the two clerics target the same creature; it would roll separate saving throws. Let's suppose it failed both separate saving throws. This would mean that the creature is "affected" by the both the spells for the duration or until one of the clerics loses concentration. The negative effects do not stack. So the creature would subtract a d4 from their attack rolls and saving throws. If one cleric loses concentration, the other effect still remains active and the creature will continue to deduct the d4 from these rolls.
This would be the same for other similar spells that cause a disadvantage of some sort, where both spells will be active but the effects do not stack in spells such as Slow.
There is an interesting point as to how do you determine what is the most "potent" effect in some cases. In such cases, I would suggest the DM decides - possibly by discussion with the player(s).
Blindness/Deafness is a great example for this. Let's suppose this spell is cast twice on the same target, once for blindness and once for deafness, but 3 turns apart and the creature fails its saving throws. When the second spell comes into effect, the target will be either blind or deaf, but not both. The DM decides which is the most potent effect here. Once the effect of the first spell ends (after a minute), the effect of the second spell will immediately activate.
As a DM, I might sometimes ask the player(s), which effect they would like to be currently active. My idea of what is "potent" might not be theirs. For instance, in the case of Blindness/Deafness, blindness might be the more potent effect in combat, but a player might think "deafness" is the more powerful effect - for example in the case where a party is stuck in a small space and they want to discuss something without their captured creature being able hear their plans.