You need to do two things to adjust the plot resolution.
First, to adjust the resolution of the image array that yt is plotting (i.e. if 800x800 for each subpanel is too low), use the set_buff_size() member function of the yt plotting class.
Next, in order to actually save it at high resolution, you will need to specify the dpi when you call savefig. Matplotlib assumes resolution-independent scaling up until the point when the plot is actually displayed or saved to disk.
Note that the dpi (dots per inch) interacts with the size of the plotting window (specified in inches). You can fully control the image resolution through a combination of calling the set_buff_size() and set_figure_size() functions that are attached to yt plotting classes.
I've made a couple minor modifications to the multiplot_2x2_time_series.py script to produce a higher resolution version. I also switched out the dataset since I don't have a copy of Enzo_64 on my laptop. Here it is:
This produces an image with a resolution of 3255 x 2760, whereas if I don't specify the dpi in the savefig call, the resolution is 1085 x 920.
Hope that's helpful,
Nathan