Question

In Sanhedrin 4 there is a dispute whether monetary cases are judged by three or by five, and the Talmud ties the dispute to whether we follow the reading or the written tradition, since it says "they shall convict." The one who holds that we follow the reading says that since it is read in the plural form, five judges are needed; and the one who holds that we follow the written tradition says that since it is written in a form that implies fewer, three judges are enough.

And Tosafot there wrote that specifically when the reading and the written tradition contradict each other, the one who holds that we follow the reading says so; but when the reading and the written tradition do not contradict each other, one can accept both. They brought proof from the Talmud in Keritot 22b, where Rabbi Akiva (who in Sanhedrin 4a holds that we follow the reading) says that if someone ate doubtful forbidden fat, even if it was only one piece, he is liable for a provisional guilt-offering. There this follows the view that we go by the written tradition, since the verse writes "commandment" in the singular and not "commandments" in the plural. Tosafot explain that since the written tradition does not contradict the reading but only adds to it — because according to the reading it applies specifically to one piece out of two pieces, whereas according to the written tradition even one doubtful piece qualifies — one can accept both.

My question is: seemingly here too, with the judges, the written tradition only adds to the reading — because according to the reading you specifically need five judges, while according to the written tradition you can already judge with three judges.