Answer: The Shulchan Aruch (OC 279:1) writes that even after a candle has gone out on Shabbos, it remains muktze for the rest of Shabbos. If one places their candles on a tray, the tray itself is considered to be a bassis¸ a base, and is rendered muktze, too (ibid. 309:4).
The Magen Avraham (277:8) and Shulchan Aruch Harav (OC 277:6; 310:16) write that if one places something such as challa on the bassis before Shabbos comes in, then the table becomes a bassis for the permissible item, too. This item must be more important than the muktze item. In this way, one would be able to move the bassis after the candles have gone out (See Shulchan Aruch 310:8). The Mishna Berura (277:18) adds that it must be an item that one needs for Shabbos. Thus, R’ Shlomo Zalman Auerbach (quoted in Shemiras Shabbos Kehilchasa 20:n216) suggests placing a bottle of wine on the table. R’ Shmuel Wosner (Shevet Halevi 8:52) explains that this prominence does not mean that it is worth more, though dependent on its necessity. As the challa or wine is needed for the Shabbos meal, it is more important than the candles that are no longer burning.
In conclusion, if one wants to move the table after the menora has gone out, one should place something important that one will later use such as challos or wine on the table before Shabbos, thereby ensuring that the table is not just a bossis for the muktze item.