In the DMG, multiple non-damage effects from a source with the same name do not stack (for example, a character with Bless cast on it multiple times only gains the benefit once).
Would this also be true for Modify Memory? If a creature has Modify Memory cast on it to alter one memory, and then cast on it again to alter a different memory, will only one casting take hold, and which one (assuming they're cast at the same level)?
The non-stacking of spells is only for effects that actually have a duration. It does not apply to instantaneous spells that inflict some permanent effect (or permanent until some other effect removes it).
The modify memory spell is a slightly strange spell in that it is composed of two components. It has a duration (concentration, 1 minute) but that only applies to the Charm effect (as it says "While this charm lasts...").
The second component of the spell allows you to modify a memory while the target is charmed, and this memory modification effect is permanent until restored. It does not depend on the spell duration and so is not affected by the "non-stacking" rule.
As soon as you finish describing memory you want to implant, spell ends and new memory takes hold. Then you are free to cast another spell: previous spell has already ended, so there is no overlap in duration.
