median filter one after the other
The median is a value of a sample which states that half of the other values of the sample have higher values and the other ones are smaller ones. In a 3⨉3 filter you are selecting the median out of a sample of 8 elements. Let's assume we have the following values in our sample (an image of size 3⨉3):

1  2   4
8  16  32
64 128 255

If we apply the median filter for the upper left value [sample: {2, 8, 16}], the median is 8 (not processing out of boundary values). After the first application of the median filter we get a new sample:

8  8  16
16 20 16
16 32 32

If we apply the median filter again, we get:

16 16 16
16 16 20
20 16 20

So my point here is that after each application of the median filter, you will get a new sample [0]. But the evaluation of one new pixel depends on all the other sample values and modifies the sample itself. Because of this dependence I cannot see any way to be able to apply the filter twice in one step. I also did not find any literature about this [1].

[0] Unless the image contains only the same value at each pixel which we cannot assume.
[1] which I don't want to use as a pro or contra argument.