Is it possible to have two liposuction procedures a week apart?

Serial liposuctions are very often done just a day apart when done under local tumescent. You recover all at once and are back to the gym 1 week later.

Doing liposuction one week apart in different areas is usually safe. I do most of my liposuction's under general anesthesia, and the biggest concern is fluid shifts. These are expected to normalize well within a number of days. The other concern is lidocaine toxicity, which becomes an issue only if that is used. If your plastic surgeon does use lidocaine, this would not be an issue at one week.

One week is not enough time to allow your body to heal after a liposuction procedure.  You will have swelling for up to 6 months after liposuction.  I would suggest waiting a full 6 months between procedures for this reason.