After looking into your question, I could find no way of changing the number of plots that are displayed on the NI Hypertrend ActiveX object by default. However, once a plot has been added by double clicking on its name in the plot legend, it will stay displayed if the VI is saved, even after restarting LabVIEW.
The closest I could come to programmatically displaying a plot is to make individual plots visible or invisible, however, this requires the plot to be displayed in the plot legend as previously mentioned -- it seems there are two properties, whether the plot is "displayed" as in the plot legend, and whether it is "visible". If the plot is "displayed" you can programmatically change the visibility, but the ActiveX control does not allow you to programmatically change whether a plot is "displayed", at least not that I could determine. The attached VI shows how to do this. you will need to alter the tags that the NI Hypertrend is trying to plot to your own tags.