If the Runner is accessing a server when an effect causes him/her to access that same server again, the second access must wait until the first access is completed before the new access can resolve. In other words, the Runner can never have simultaneous multiple accesses of the same server.
I was wondering if you could help me through a particularly tricky thought exercise that results from the "cascading triggers" rules. Let's say that you're the Runner and you've got installed, along with 2 , and 2 s. You do a run on R&D, pass all of the ice, access the top card and it's s. You score the agenda, the corporation takes a bad publicity. The bad publicity triggers Raymond Flints ability, and you need to access 3 cards from HQ. It seems to me you set the top card from R&D aside, and return to it when you've finished resolving this trigger from Raymond Flint. Raymond Flint has fully resolved, you go back to accessing the next two cards from R&D. Is this correct?
So let's say you begin accessing 3 cards from HQ as a result of Raymond Flint triggering. Your first card is a , so you take 1 net damage, but you can't afford to trash the card, so you set it aside to continue accessing. Your second access from HQ is another Vulcan Coverup. You score the agenda, the corporation takes a bad publicity. The bad publicity triggers Raymond Flint's ability again. So again, if the above is correct, we'll access 3 cards from HQ. This is the part that is a bit trickier. Should I return the Shock! back to HQ for this access, or should it stay separate from cards I can now access?
If the Shock! isn't added back to HQ for this second subset of accessing HQ, then lets say we access 3 Ice. That access is done, so we fall back to the previous access to HQ that we have 1 remaining from. We access an Ice, then fall back to the R&D access we started with. We've already seen and scored the top card, so we continue to see the next two cards.
If the Shock! is added back to HQ, there is a chance that our next 3 accesses could see it again and take 1 damage. Then, once that access is done, we've already accessed the Shock! on the previous Raymond access. Should Shock! be set aside as a card we've already accessed? We access 1 more card, then roll back to the R&D access we haven't finished.
I know it's not a very common situation to find ourselves in (maybe it will be with the release of the upcoming ). As far as I know, we don't have precedent on stopping mid-access to access other cards, or from the same set of cards (when Raymond Triggers from R&D it seems accessing HQ mid access isn't as big of an issue as Raymond triggering during an HQ access).