gistfile1.txt

scala> object Thing1 {  
     | var things = 0
     | }
defined module Thing1

scala> class Thing1 {
     | Thing1.things +=1 
     | }
defined class Thing1

scala> object Thing2 {
     | var things = 0 
     | }
defined module Thing2

scala> class Thing2 {
     | Thing2.things += 1
     | }
defined class Thing2

scala> case class Combo(t1: Thing1, t2: Thing2)
defined class Combo

scala> val c1 = Combo(new Thing1, new Thing2)
c1: Combo = Combo(Thing1@5b55c5eb,Thing2@5c34f625)

scala> Thing1.things
res0: Int = 1

scala> Thing2.things
res1: Int = 1

scala> val c2 = c1.copy(t2 = new Thing2)
c2: Combo = Combo(Thing1@5b55c5eb,Thing2@7525c6bd)

scala> Thing1.things
res2: Int = 1

scala> Thing2.things
res3: Int = 2