Can you duplicate and move objects in a sequence?

It is possible but it takes a bit of setting up the Sequencer. By default the Sequencer is storing the world transform of the objects, meaning it won’t take into account that you’ve moved things to a new location. The Sequencer needs to be configured to work additively instead, storing just the transforms relative to whatever location the actor has.

You can change the actors assigned to a Sequencer by right clicking the main track, and assigning your other actors to it instead.

If you add an Additive track (click the Section button on the track) to a Transform track (delete the existing non additive Transform track while you are at it), and then enter just the difference in value it will just add to the current location and rotation of where the object is located.

In my case I changed Z 0 to Z 600, meaning any mesh I run this Sequencer on goes from current position to 600 units above current position, wherever in the world it is located.
The first key I have has 0 0 0 for XYZ location.

The second key has 600