I used to have a client callable SI that would then call a server side only SI.

Also believe this used to be the "best practice" a few years ago?!

That way the server side script is always invoked with an argument that is passed on through the client side one with a parameter.

It does add the "extra" SI complexity to the solution, but as mentioned by Frantisek, we should try to maintain the server side SI as a set of reusable core tools, and have the client callable SI working somewhat as a service provider.