You can grow squash, cucumber, melons.. vine plants in general as long
as you provide some means of support. One recommended support (? from
Bob Thompson of The New Victory Garden?) is used pantyhose; the fruit
is cradled in the toe/foot area. Strong and lightweight, etc.

My tomato cages are industrial strength, i.e. concrete reinforcing
wire. Tomatoes are up to my shoulder as of today (zone 5 Iowa).