Problems converting a constant

I have a vbs file which contains a huge list of constants e.g

Private Const Client = 3

The problem I am having is that I need to change one of these constants into a variable populated by a function call. e.g

Private Const Client = MyFunction()

Naturally this will not work as it is a constant but I cant declare it as :

Dim Client
Client = MyFunction()

because on a million pages which include this file and refer to this variable they will find that Client = nothing.

Why cant I do this :

Dim Client = MyFunction()

There is no option explicit on my page although maybe the many pages including this file may have it on which I cannot change.
Any ideas how I can get around this?