Sorting a data frame in R by multiple columns at the same time

So I have a large dataframe (7000 rows) that looks like this:

head(mx)

                        Stem Progenitor   Astrocyte   Neuron genename
ENSRNOG00000000007 0.0517698   0.700234  0.11753300 4.591050     Gad1
ENSRNOG00000000010 0.0536043   0.471518  0.00741803 2.280760    Cbln1
ENSRNOG00000000012 0.0163017   0.285178  1.89533000 0.268405    Tcf15
ENSRNOG00000000024 2.7904200   0.703727 13.96940000 4.944650    HEBP1
ENSRNOG00000000028 2.5059900   2.563040  4.83952000 0.840013     Nde1
ENSRNOG00000000029 1.6204500   2.928300 15.58360000 1.750350    Myh11

      

        
        
        
      

    

I need to sort this dataframe in such a way that it is ordered from maximum to minimum by whatever value in the first four columns. So, for example, sorting for these 5 lines would be:

                        Stem Progenitor   Astrocyte   Neuron genename
ENSRNOG00000000029 1.6204500   2.928300 15.58360000 1.750350    Myh11
ENSRNOG00000000024 2.7904200   0.703727 13.96940000 4.944650    HEBP1
ENSRNOG00000000028 2.5059900   2.563040  4.83952000 0.840013     Nde1
ENSRNOG00000000007 0.0517698   0.700234  0.11753300 4.591050     Gad1
ENSRNOG00000000010 0.0536043   0.471518  0.00741803 2.280760    Cbln1
ENSRNOG00000000012 0.0163017   0.285178  1.89533000 0.268405    Tcf15

      

        
        
        
      

    

I know that I can sort a dataframe one column at a time using a command like:

mx <- mx[with(mx, order(-Stem, -Progenitor, -Astrocyte, -Neuron)),]

      

        
        
        
      

    

But this in the above example puts Tcf15 above Gad1 and Cbln1. Is there a way to sort by the highest value in any of the four columns? I could write some script to do this, manually iterate over the dataframe and sort into a new dataframe using Rbind, but this is terribly inefficient and I'm sure there is a better way to do it.