Is cypress support cross browser testing like selenium or is there any limitations

I am wondering is the cypress support many browser types and version to implement cross browser testing. As they mentioned at there documentation [1] they do support Chrome-family browsers (including Electron) and beta support for Firefox browsers.

But do they support internet explorer, safari and other version of chrome and Firefox. If not is there any alternative way to implement such facility. (external plugin or something). I have tried the Applitools Ultrafast Grid.[2] But their configurations (APPLITOOLS_API_KEY) mentioned only for windows and mac OS. I'm implementing the project at Ubuntu OS.

And also cross browser test should run in the header less mode.

[1] https://docs.cypress.io/guides/guides/cross-browser-testing.html#Continuous-Integration-Strategies

[2] https://applitools.com/blog/cypress-cross-browser-testing?utm_referrer=https://www.google.com/