You can certainly have more than 9 tags on i3. In fact you can have tags with arbitrary names. They are a bit more difficult to manage with the default config, because only the default 9 have keybindings. But you can create your own tags and bind keys to assign windows to them or switch to them with a custom config.

You can also use a tabbed window layout (Super + E) to keep multiple programs full-screen on one tag. Then you can switch between them with the tabs at the top or Super + J, Super + ;.