I can think of one course local to me, Bramhall, not Bramall Park, which has two tracts of parallel holes: the 1st, 4th, 10th, 18th and 9th; the 5th, 6th, 7th, 8th, 11th, 12th, 13th, 14th, 15th, 16th and 17th! Yet it is not at all a dull course, with tons of variety and many memorable holes. I don't know which architects have been involved in the design, but the club's 70th anniversary booklet detials the many trials and tribulations of the acquisition and loss of umpteen parcells of land, particularly in the inter-war years.
The championship course at Bromborough has a spread of 11 parallel holes - again it's a good course.
The 9-hole course at Cheadle (dating back to 1885) is essentially 5 parallel par-4 holes with three of the four par 3s running at right angles to them. That's the shape of the land they have. You couldn't do much else, really, but it's a nice course, if rather restricted. They credit R Renouf as the architect who was presumably a relation of Tommy Renouf, one of the Jersey School, who was professional at Manchester and, later, Stockport, designing a number of courses in the area.
Chester is really 17 parallel holes with only the par-3 3rd at right angles to them. It's not a great course but it is more varied than my desciption might imply, as there is a cliff running the length of the course with a number of holes making good strategic use of it.
Davenport is quite a recent course (1973) yet no-one there knows who designed it! Like Chester it is in two tracts of essentially parallel holes, but because these run across rising ground there is rarely a feeling of monotony.
An aerial of Delamere Forest (sorry, it's fuzzy on Google Earth) would reveal that all but two or three holes run in the same (or opposite) direction, but I don't suppose you'd notice! It's a gem of a course (Fowler).
Actually, looking at my old Cheshire book I notice there are dozens of courses with a large number of parallel holes. On of the few on which you really notice it, though, is Upton-by-Chester and I'm afraid dull architecture and a rather plain site have to answer for that.