The Gemara in Pesachim (13a) writes that R' Elazar Ben Yehuda from Bartosa says that if the day before Pesach falls on Shabbos (when one can't burn Chametz), one should destroy all his Chametz on Friday. This includes Teruma which became impure Biblically, out of doubt, and even pure Teruma which he won't have time to eat.
The Rabbis said that pure Teruma shouldn't be burnt (one isn't allowed to destroy Teruma). R' Elazar asked them why not, as it will have to be destroyed anyways. They answer that there may be guests who are hiding outside the city wall who will come on Shabbos and you will be able to feed him some of the Teruma. R' Elazar asked that if we worry about such far-fetched cases, why not then say that perhaps Eliyahu will come and inform us that the Teruma that's Tamei out of doubt is really pure.
The Rabbis said that we know that Eliyahu won't come on Erev Yom Tov.
However, if one looks at a parallel quote in Eiruvin (43b) which says that Eliyahu won't come on Erev Shabbos and Erev Yom Tov since we're going to have to greet him and won't have time to prepare for Shabbos.
So why can't Eliyahu come on a Shabbos Erev Yom Tov? One can't do any hachana (preperations) on Shabbos anyways.