Q. What is one supposed to do after the seder with the wine from Kosh Shel Eliyahu?
A. Sefer Chag Hamatzos (35,22) quotes a number of Authorities (Hagodas Chakal Itzchok – Beer Yehuda et. al.) that report the minhag of pouring the Kois shel Eliohu, after reciting Shfoich Chamoscho, into the cups of the participants. They will use it then for the 4th. Kois.
Minhogey Hasam Soifer (10,7), using the same approach of "adding another Mitzva, to the one already done", advises leaving the cup covered until the next morning and using it for the Kidush of the day.
Seifer Vayaged Moishe (30), combines both traditions. After Shfoich Chamoscho the remains are poured into the cups. Then the Kois Shel Eliahu is replenished and left for Kidush Hayom.
Nitey Gavriel, however, mentions the opinion of R.S.B. of Lubavitch and Rav Yakov Landa Zt"l (Rab"d of Bnei Brak), of pouring it back into the bottle, after adding a bit of wine to the cup, (for non-pogum purposes). The opinion of Horav Shlomo Miller Shlit"a is also to pour it back into the bottle, when it can't be saved for Kidush Hayom.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a.
I cannot understand the reasoning of the 4th opinion of adding wine to the cup, for non-pogum purposes. Nobody has drunk from the cup. Therefore, the cup is not pogum. Unless they are giving credence to the idea that we were told as children, that Eliyahu HaNavi sips from the cup when he slipped in unnoticed during Shefoch. In that case it would be necessary to pour in a bit of wine before Kiddush in the morning according to the 2nd opinion and before the drinking of the 4th cup according to the 3rd opinion.