How I interpret these questions using the letter of the law:
Glossary, cumulative wrote:If a card is cumulative, multiple copies of the card can have the same effect on the same target(s) at the same time. Damage markers (Tactic cards) are cumulative, as are cards specifically marked "cumulative." All other cards are not cumulative.
The following section clarifies "effects" and "targets" with a few examples, and also adds this
Multiple responses to a single action (such as a battle) generally resolve one at a time, and thus are not restricted by cumulativity rules (unless they generate a continuing effect).
With this in mind:
FranklinKenter wrote:Can you play multiple copies of Borg Kiss triggered from the same assimilation?
I'm not sure which use of Borg Kiss you're referring to. For the second use it's absolutely clear, you can play as many Borg Kisses as you like. For the first, I don't think the cumulative rule is even relevant. You play the first Kiss, you draw the probe card and probe again. If you play the second Kiss as a "just" response to the second probe, then it's a different target so the cumulative rule doesn't apply and you can re-draw and re-probe. If you try to play the second Kiss as a "just" response to the first probe, the target is invalid ("the probe card" was drawn into your hand by the first Kiss and you can't draw it again) so you can't get past initiation (step 1 of the action).
FranklinKenter wrote:Can you play multiple copies of Double Dumbass on You! triggered from the same stop?
Yes. This falls under the "multiple responses to a single action" clause cited above; each Dumbass targets a different group of personnel, so you never have multiple Dumbasses trying to stop the same personnel at the same time.
FranklinKenter wrote:Can you play multiple copies of Baseball triggered from the same commandeering?
You can play as many Baseballs as you want,
but you only score points from one of them. The "target" is you as a player, and the "effect" is scoring 20 points. This is a continuing effect (cf. the quoted text about multiple responses), and at any point in time only one Baseball can have that effect on you. This is also a direct analogy to the Process Ore example in the cumulative rule, except with points as the effect rather than draws.
FranklinKenter wrote:Can you play multiple copies of Dixon Hill's Business Card (as an interrupt) to capture multiple personnel triggered from the same death?
Yes, same as Double Dumbass.
FranklinKenter wrote:Can you play multiple copies of Honor Challenge in battle to have each Honor Klingon kill multiple opposing personnel?
Yes, same reason.
A proposal if these rulings are objectionable:
The answer to all of these questions would be "no" if all "just" actions are treated as occurring "at the same time" for the cumulative rule. I have not thought about broader implications of such a ruling.