Luke records Jesus healing a crippled woman:
10 And he taught in one of their synagogues on the Sabbath days. 11 And behold, there was a woman who had had a spirit of infirmity for eighteen years, and was stooped over, and could not lift herself up at all. 12 When Jesus saw her, he called her to him and said to her, Woman, you are delivered from your disease. 13 And he laid his hands on her, and immediately she was made straight and glorified God. 14 But the leader of the synagogue responded with indignation because Jesus had healed on the Sabbath day, and he said to the people, There are six days in which men ought to work; in them come and be healed, and not on the Sabbath day. 15 Then the Lord answered him and said, Hypocrite, does not each one of you on the Sabbath day loose his ox or his donkey from the stall and lead it to the water? 16 And ought not this daughter of Abraham, whom Satan has bound now eighteen years, be loosed from this bond on the Sabbath day? 17 And when he said this, all his adversaries were ashamed. But all the people rejoiced for all the tremendous deeds that were done by him. (Luke 13 NMB)
From the details it is clear Jesus was in one of the synagogues (ἐν μιᾷ τῶν συναγωγῶν) and there was only one woman who was healed. The leader of the synagogue was upset because Jesus had done this on the Sabbath (singular - verse 14 twice). Jesus defended His actions on the Sabbath (singular - twice verses 15 and 16).
Since one woman was healed in one synagogue on one Sabbath, why does Luke introduce this episode using the plural Sabbaths, saying ἐν τοῖς σάββασιν, on the Sabbaths?
[Note: In discussing this with someone who thinks this question should be closed I pointed out that preserving the literal text leads to something like He was now teaching in one of the synagogues on the Sabbaths..." which could be a way to say on multiple Sabbaths Jesus taught in the same synagogue. Perhaps the meaning is inconsequential here but does function as a way for Luke to show he recognizes the difference between σάββατον and σάββασιν.]