ASP.NET MVC 2 - Binding To Abstract Model

If i have the following strongly-typed view:

<%@ Page Title="" Language="C#" MasterPageFile="~/Views/Shared/Site.Master" Inherits="System.Web.Mvc.ViewPage<XXX.DomainModel.Core.Locations.Location>" %>

Where Location is an abstract class.

And i have the following Controller, which accepts a strongly-typed Model via a POST:

[HttpPost]
public ActionResult Index(Location model)

I get a runtime error stating "Cannot Create Abstract Class

Which of course makes sense. However - i'm not sure what the best solution is here.

I have many concrete types (around 8), and this is a view where you can only edit properties of the abstract class.

What i've tried to do is create overloads for all the different concrete types, and perform my logic in a common method.

[HttpPost]
public ActionResult Index(City model)
{
   UpdateLocationModel(model);
   return View(model);
}

[HttpPost]
public ActionResult Index(State model)
{
   UpdateLocationModel(model);
   return View(model);
}

etc etc

And then:

[NonAction]
private void UpdateLocationModel (Location model)
{
   // ..snip - update model
}

But this doesn't work either, MVC complains the action methods are ambiguous (also makes sense).

What do we do? Can we simply not bind to an abstract model?