Can I run plain TeX on Overleaf?

Yes — you can configure your project to be compiled using plain TeX by the following:

1. In the Overleaf editor, click on the "Settings" button (i.e. the gear icon next to your username in your project window).
2. From the "LaTeX engine" dropdown list, select "LaTeX dvipdf". Then click "Save settings".
3. Add a blank file to your project, and save it as latexmkrc (if you do not already have this file).
4. Add the following line to your latexmkrc file:

$latex = 'tex %O %S';

If you want to use xetex, pdftex or luatex instead, leave the "LaTeX engine" on "Automatic", and use in your latexmkrc file:

$pdflatex = 'xetex %O %S';