Moving points together along a specified path

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Dear all,
I have a question regarding the displacement of a point through time along a specified path.
For example, I created a moving point, along the following path as presented in the figure below:
This is fine, the point is moving along the path as I wanted.
However, now I would like to move more than one point (two or more), side-by-side along the same path.
For example respecting the following configuration:
If fact, I want that that group of 3 points move together along the specified path.
Thank you in advance for your help,
All the best

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