I would like to plot 66 datasets and show their legends. Unfortunately, according to the MathWorks Support Team, MATLAB legends are limited by default to 50 entries.
I tried the workaround they suggested that involves making another axes in the plot, copying the previous data, and then hiding the new axes, but I couldn't get it to work (the new axes only shows 1 additional variable from the 16 that are left), and so I'm stuck.
Are there any other ways to display more than 50 legend entries?

As implied by Cris's comment, it's likely that your plot is going to be very unclear - if you need 50+ legend entries then you've got 50+ different line styles, which is pretty crazy from a usability perspective.
That aside, you can achieve an unrestricted legend using the
gridLegendFileExchange submission.Output: