Moving points together along a specified path

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