You may be thinking of Philip José Farmer's [*Dayworld*](http://www.goodreads.com/book/show/16543.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.<br>
> 
> The sequels are Dayworld Rebel, '87 & Dayworld Breakup, '90.