I can think of two easy ways to handle this problem.  

1.

Send a message via the QueryString in your Server.Transfer call:
Server.Transfer("SomePage.aspx?s=1");

And in the page you transferred to:
   
if (Request.QueryString["s"] != null)
{
  switch(Request.QueryString["s"])
  {
     case "1":
        this.lblMessage1.Text =
((TestSender_1)Context.Handler).SenderName;
        this.lblMessage2.Text =
((TestSender_1)Context.Handler).Message;
        break;
     case "2":
        this.lblMessage1.Text =
((TestSender_2)Context.Handler).SenderName;
        this.lblMessage2.Text =
((TestSender_2)Context.Handler).Message;
        break;
     default:
        this.lblMessage1.Text = "No Sender";
        this.lblMessage1.Text = "No Message";
        break;
  }
}

Where lblMessage1 & lblMessage2 are labels on SomePage.aspx and
SenderName and Message are public properties on the sending pages
(TestSender_1 & TestSender_2).

2.  

If you are going to be transferring from many pages and the properties
are going to be the same you can implement an interface on the page
that does the Server.Transfer.  (I'd choose the QueryString
implementation over this however.)

public class SenderPage : System.Web.UI.Page, IMessage {}

In the case of this example the interface IMessage will contain
SenderName and Message and the implementing pages contain the code for
such.

The code on the page you transfer to will should look similar to this:

this.lblMessage1.Text = ((IMessage)Context.Handler).SenderName;
this.lblMessage2.Text = ((IMessage)Context.Handler).Message;

Well, hope that helps.
-Peter