set.seed(42)
DF <- data.frame(key1=sample(letters[1:2],10,TRUE),
                 key2=sample(letters[1:2],10,TRUE),
                 key3=sample(letters[1:2],10,TRUE))

DF <- within(DF,{newkey <- interaction(key1,key2,key3,drop=TRUE)
                 levels(newkey) <- paste0("key",seq_along(levels(newkey)))
                 })

#    key1 key2 key3 newkey
# 1     b    a    b   key4
# 2     b    b    a   key2
# 3     a    b    b   key5
# 4     b    a    b   key4
# 5     b    a    a   key1
# 6     b    b    b   key6
# 7     b    b    a   key2
# 8     a    a    b   key3
# 9     b    a    a   key1
# 10    b    b    b   key6

library(data.table)
as.data.table(DF)[, combined := .GRP, by = names(DF)][]
#     key1 key2 key3 combined
#  1:    b    a    b        1
#  2:    b    b    a        2
#  3:    a    b    b        3
#  4:    b    a    b        1
#  5:    b    a    a        4
#  6:    b    b    b        5
#  7:    b    b    a        2
#  8:    a    a    b        6
#  9:    b    a    a        4
# 10:    b    b    b        5