Running Lead Source that Updates Data Value, Instead of Replacing

We created a new field that we hoped would allow us to have a running tab of lead sources. We called this the "Running Lead Source". I had hoped that if we triggered the campaign with every Lead Source change to update the Running Lead Source with "{{lead.Lead Source}}, {{lead.Running Lead Source (L)}}" that would allow us not to lose the data already collected in the Running Lead Source field. However, I do not believe this is working.

Is there a way to update the field without replacing the current value? If not, there should be.