We've been using the GIS Request Management Solution for 9 months and this is also something I wish we were able to do, but was told it's currently not possible without duplicating the task.
You can update the 'Assignee' for an existing activity when it reaches a certain stage. E.g., John completes step 1, re-assigns to Jane to complete step 2
If it's a larger project, break it up into multiple activities and assign them to each person. E.g., John is assigned activity 1, Jane is assigned activity 2. We've had customers create a "project" field to be able to break up projects into activities but still be able to track/filter the overall project.
Add a field/filter for second assignee, third assignee, etc. This will take some more work/configuration of the layers/dashboards on the back end.
