As I understand it, the Passover meal (at least in modern times, and probably in Yahshua's time as well), incorporated within it "4 cups" which were specially set aside for certain times of the meal. This phrase does not mean a literal number of cups, but rather a literal number of special significances to the drinking of each person's own individual cup. We'd say in modern parlance, "four toasts".
If memory serves, there were two cups before the main meal and two afterwards, with the fourth and last one serving to close the meal, much like a closing prayer closes most church assemblies in our Western Church of Christ culture. The four cups, or toasts, each have special meaning: "I will bring out," "I will deliver," "I will redeem," and "I will take".
Luke, in chapter 22, refers to two of these four cups, one before the main meal, probably the first one as that serves more as an introduction to the meal, which is implied with Yahshua's comments about being happy to eat the meal with them, and since it's a cup of blessing, and one after the meal, probably the third cup, that of "redemption" -- "I will redeem" -- a cup of blood for a new covenant.
Paul also refers to the "cup after supper", in 1 Cor 11:25.
So Yahshua was not saying, "Take this physical cup and share it amongst yourselves"; he was saying, "Take this cup and participate in it amongst yourselves; I'm not participating in it until the kingdom of God comes".
Each person had his own cup, just as each person had his own plate. But at four times within the meal, everyone drank at the same time in a symbolic "toast" to the meaning of that drink.
There's a LOT of fascinating material in the Passover meal that we non-Jews have missed. For example, three pieces of Matzah bread (crackers) are placed in a three-pocketed cloth, one piece per pocket (think Father, Son, Holy Spirit), and at a certain point in the meal, the middle piece is taken out, broken in half, half is wrapped in a linen cloth and hidden while the other half is put back in the pocket, and after a while, the kids are sent to find the hidden piece. The kid finding it brings it back to Papa for a small redemption (a dollar, or a piece of candy, etc), and then that piece is distributed out to everyone to eat a grape-sized piece.
Tell me you don't see Yahshua's body broken, wrapped in linen, hidden in a tomb for a while, redeemed, and shared by his disciples in the Passover.
It's also interesting to note that Matzah is pierced, and those piercings are in stripes ("he was pierced for our transgressions"; "with his stripes we are healed" - Isa 53:5, NIV, KJV).
Near as I can tell, Yahshua intended for his followers to continue celebrating the yearly Passover, but now, instead of it celebrating the deliverance of Israel from Egyptian slavery, it would celebrate the death of Yahshua and the delivery of his New Israel from slavery to sin and death. But in our withdrawal from Law-keeping and Judaizing, we rode the pendulum too far and have divorced ourselves from a lot of culture that would be enlightening to us and which I believe Yahshua intended us to use for our educational and spiritual growth.