Without a fuller picture of what's in your wallet, please take the following with some caution.
Regarding your SW Plus card, which you say renewed in December and for which you already paid the annual fee, Chase's policy is to allow cardholders a period of 30 days after your annual fee is billed to cancel their card and request a refund. Billed means when the annual fee posted to your statement, not when it was paid. After 30 days, you'll get some mixed data points that say Chase may refund you a prorated amount.
You may want to keep your SW Plus card open while you are trying to apply for two more cards from Chase, because your Plus card has a credit line that is presumably propping up your credit score (available credit, utilization %), and you could offer to reallocate credit from the Plus to a new card if Chase is on the fence about approving more cards because they feel they've already extended you too much credit.
Which two cards are you planning to double dip with your last slot? The SW Premier and ...? I ask because there may be certain rules a general instruction may miss. I can follow up with instructions how to do it.
Please note that if you double dip, you're getting two bites at the apple, not a free bite. So those two cards at 4/24 will bring you to 6/24 and you very likely won't be under 5/24 again in November 2018. The sixth card essentially gave you a shot at one of Chase's cards early, and will push when you'll be under 5/24 again out to the next oldest card.
