Pass parameter to controller, not method inside controller. MVC 5 c#

I'm looking to see if there is anyway to pass a parameter to the controller itself and not a method inside the controller.

I use named connection strings with parameters for my ADO.NET models. This means I must pass a parameter every time I call the model

MyEntities myentity = new MyEntities(Param);

We do this because each division in our company has it's own mirrored SQL server and when using data we want the local divisions data.

The problem I face is that I cannot put the connection to the Model outside of a Method because it requires a parameter.

What I currently have to do is this

namespace WebApps.Controllers
{
    public class MyController : Controller
    {
            public ActionResult Index(string Param)
            {
                MyEntities myentity = new MyEntities(Param);
                var db = myentity.table;
                return View(db);
            }
    }
}

What I'd like to do is this...

namespace WebApps.Controllers
{
    public class MyController : Controller
    {
        MyEntities myentity = new MyEntities(Param);

            public ActionResult Index()
            {
                var db = myentity.table;
                return View(db);
            }
    }
}

This would also allow me to properly use a dispose method. I can't currently use it because I need to pass that parameter to close the db. (it doesn't exist outside the method)

This fails...

protected override void Dispose(bool disposing)
    {
        if (disposing)
        {
            this.Dispose();
        }
        base.Dispose(disposing);
    }

Could anyone tell me if passing a parameter directly to the controller is possible?