You may be thinking of Philip Jose Farmer's Dayworld trilogy, first published in 1985.

From the Goodreads link:

Dayworld leads a sf trilogy by Philip José Farmer set in a dystopian future in which an overpopulated world allocates people only one day a week. The other six days they're in suspended animation. The focus is on Jeff Caird, a daybreaker living more than a day a week. He's not like most daybreakers. He belongs to the radical Immer group working to create a better government. Not all Immers are daybreakers, but send information from one day to the next they've daybreakers like Jeff. Immer daybreakers assume seven different personalities & jobs, slipping from culture to culture in seven different worlds. While Jeff & the other six go day to day, they run into problems while working as Immer daybreakers. They must cover their tracks while trying to keep up with seven different lives, families & jobs. It could drive a man crazy. It does & the Immers must dispose of Jeff to keep the rest safe. Jeff, wanting to live, tries to escape, but they have undercover Immers in every job & government level. Jeff is caught & put in an asylum, classified with multiple personality disorder. If considered incurable he'll be killed. But Jeff has an escape plan.

The sequels are Dayworld Rebel, '87 & Dayworld Breakup, '90.

You may be thinking of Philip José Farmer's Dayworld trilogy, first published in 1985.

From the Goodreads link:

Dayworld leads a sf trilogy by Philip José Farmer set in a dystopian future in which an overpopulated world allocates people only one day a week. The other six days they're in suspended animation. The focus is on Jeff Caird, a daybreaker living more than a day a week. He's not like most daybreakers. He belongs to the radical Immer group working to create a better government. Not all Immers are daybreakers, but send information from one day to the next they've daybreakers like Jeff. Immer daybreakers assume seven different personalities & jobs, slipping from culture to culture in seven different worlds. While Jeff & the other six go day to day, they run into problems while working as Immer daybreakers. They must cover their tracks while trying to keep up with seven different lives, families & jobs. It could drive a man crazy. It does & the Immers must dispose of Jeff to keep the rest safe. Jeff, wanting to live, tries to escape, but they have undercover Immers in every job & government level. Jeff is caught & put in an asylum, classified with multiple personality disorder. If considered incurable he'll be killed. But Jeff has an escape plan.

The sequels are Dayworld Rebel, '87 & Dayworld Breakup, '90.