Install the spec kit to be used with multiple coding agents for the same project?

[cryptotomte]

Is it possible to install the spec kit for multiple coding agents for one specific project?

For example, I use github copilot, claude code and gemini-cli and jump between them when developing the different parts.
So would it be possible and if so, what contstraints should I be aware of? Like I saw on localdens latest "under the hood" video that /plan created a copilot-instructions.md file, and the same would be if the kit were installed for claude code...