HOW TO MOVE MULTIPLE HANDLES AT ONE TIME

Depends on what exactly you are going to do.

To a certain degree you may use the Scale tool or the Free Transform tool.

Jessica,

There are certain inherent ways to select and move pairs together when they belong to the same segment, but that would only be both at once, rather than all.

The plugin VectorScribe can do that with its PathScribe tool and I think the plugin Xtream Path can do it too, but Illustrator can't.

Can you tell us more about the situation that maskes it necessary? Maybe there are other ways.