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On the business plan (25/mo) you can run any plugin or theme, or custom code. You also have full SSH/SFTP and wp-cli access.

That plan actually looks really reasonable. I'm pretty sure when I last looked at it many years ago that stuff wasn't possible.

Thanks for WordPress - it's great. I think I first started 'using' it around 2006/2007ish.

Can it run custom plugins?

Yes. You can deploy your custom plugins and themes.