Rest alternating row fill in table that flows across frames — is it possible?

I have a table with 15 rows with alternating fill that flows horizontally across three linked frames.

As the table break happens on an odd row, the banding in the second frame starts with a light row.

Is there a way to make the banding in the second column match the other two — dark, light, dark, light, dark — without breaking the overflow connection between the three frames?