It is possible to work 6 days constant.
Say you work 9am to 5pm during the week. You could do a Saturday every week if you started at 4am and finished at 11am. Effectively you are getting the rest of Saturday off (13 hours), all of Sunday (24 hours) and then the 9 hours until 9am Monday morning. Grand total of 46 hours rest (only 45 required).
The problem may be that transport is unpredictable so a guaranteed finish time is rare. A fruit and veg run or a milk run are the types of jobs I can think of that may suit.