Multiple labels in one axis

I am plotting some data from a file that is being added to all the time.
The file is reread by gnuplot every 60 seconds. The data are organized in
two columns: the left column is a timestamp, that will be used in the x
axis, whereas the second column is another meaning (whose meaning is not
relevant to this discussion) that will go in the y axis.

As things stand right now, I got gnuplot to draw a tic in the x axis every
86400 seconds (one day) worth of input data, with each tic labeled with the
name of the day of the week. I would like to enhance this by labeling every
Sunday with a additional text, corresponding to the week number from the
start of the year, and the beginning of a new month with the name of the
new month.

I think I would know how to get gnuplot to do those three chores separately
- but I don't know how to get them working together, in the same x axis for
the same, constantly updated, plot. Any pointers on how to do this with
gnuplot 5.* would be appreciated.

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