I think people might have guessed this anyway based on Wedding Ellie's zones and reading the skill text closely, but just clarifying:

You can't stack the Force Strike effect that changes her Force strike (Altered Strike), but you can overlap the zone from the Force Strike Aura to have 2 buffs.

So you can't S1, force strike to get Altered Strike, S1 again, then Force strike to have 2 Altered Strikes ready, you're still left with 1 Altered Strike effect and 1 zone to cast (this is what the help text refers to).

You can, for example, S1, get Altered Strike on her, get your S1 ready, then Force Strike, S1, Force Strike, to have 2 buff zones at once, which stack with 2 buff icons on affected characters, and increases damage 50%.

Not sure what the max stack would be with multiple Cloe's.