Place the potato cubes, turkey, carrot, pickle relish, celery and crushed pineapples in a large mixing bowl. Toss lightly but thoroughly to distribute the ingredients well.
Add about half a cup of mayonnaise and toss until every piece of solid is coated with mayo. If the salad appears too dry, add more mayo, a couple of tablespoonfuls at a time.
Now, the seasonings. Since the potatoes were cooked in salted water, start seasoning by not adding any salt at all but only some ground white pepper. The sugar may not be necessary if you’re using sweet pineapples. Stir everything thoroughly.
Taste. Add salt and sugar, if needed, and stir again.
Cover the bowl with cling film and chill for at least an hour. This will allow the potatoes and the turkey to absorb the mayo. Chances are you will need to add more mayo after an hour. This is also the best time to taste the salad to determine if you need to add more salt or sugar or pepper, or all of them. So, adjust the seasonings, add more mayo, toss well, re-cover and chill until ready to serve.
Serve the turkey, potato and walnut salad on a bed of lettuce sprinkled with parmesan cheese.