Perhaps something like this?
> df<- data.frame(a=rev(1:10), b=rep(c(2,1),5), c=rnorm(10))
> df
a b c
1 10 2 -0.85212079
2 9 1 -0.46199463
3 8 2 -1.52374565
4 7 1 0.28904717
5 6 2 -0.91609012
6 5 1 1.60448783
7 4 2 0.51249796
8 3 1 -1.35119089
9 2 2 -0.55497745
10 1 1 -0.05723538
> with(df, df[order(a, b, c), ])
a b c
10 1 1 -0.05723538
9 2 2 -0.55497745
8 3 1 -1.35119089
7 4 2 0.51249796
6 5 1 1.60448783
5 6 2 -0.91609012
4 7 1 0.28904717
3 8 2 -1.52374565
2 9 1 -0.46199463
1 10 2 -0.85212079
The order function can take multiple vectors as arguments.
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