The group began broadening its focus from its traditional fast-fit operation in 2004.
It is expected to end the roll-out at the end of this year, with 410 major sites providing servicing and MoTs from Monday to Saturday.
A third of the centres will extend provision to Sundays.
“Most customers don’t want routine maintenance done on Sundays, but ultimately it will come,” said Mike Wise, head of Kwik-Fit Fleet.
Kwik-Fit centres carry out 8,000 MoTs weekly.
Last year it added windscreen replacement services and air-conditioning system recharging at all sites.
A spokesman said the roll-out has been gradual because some centres needed to be extended for the extra bays required, and planning permission has been required.
In March, Kwik-Fit’s network gained the BSI PAS 80 Kitemark for vehicle workshops.