Rosh Hashanah 29b
R. Akiva Yosef Schlesinger zt”l the son in law of R. Hillel Lichtenstein zt”l (Kolomai) tried to convince the Gedolim to blow Shofar on Rosh Hashana that falls on Shabbos.
He claimed, R. Shmuel Salant and the Aderes both agreed with him.
In the years 1904 &05 Rosh Hashana fell on Shabbos. He tried to organize for a Sephardic & Askenazi Bais Din to sit at the Churva Shul and to blow Shofar. For some reason the opposition was too strong and it never materialized.
One of his arguments was, The Rif is the one, who holds to keep two days R.H. in Eretz Yisroel. We all follow his Psak. It is the same Rif who holds*, where there is a Bais Din sitting you do blow Shofar on Shabbos Rosh Hashana. (R.Y.B. Zakai) If we rely on the Rif not to put on Tefillin on the second day R.H., then for sure we can rely on his Psak to blow Shofar on Shabbos.
It is interesting, in the Cairo Genizah they found a Piyut, describing blowing Shofar on Shabbos, by attaching the Shofar to a pillar and the Ba’al Tokeah putting his mouth to the Shofar without holding it in his hands.
The Rif set up a Bais Din in Fez and blew Shofar on Shabbos.