Use it to link related ideas showing cause and effect or reason and result. She couldn't attend the meeting; by the same token, her absence affected the decision-making process.
Pro Tip 2/3
Equal Comparison
It highlights that what applies to one case also equally applies to another. The rule is strict for employees, and by the same token, it must apply to management.
Pro Tip 3/3
Avoid Overuse
Use sparingly to maintain impact. Overusing it may confuse the reader or listener. He excels in math; she in literature. But don't say 'by the same token' for every similarity.