Yes, the .Net philosophy with regards to proper layered
distributed design does address that dilemma, and I have
dealt with this in the past as well.

Basically this is my recommendation:
1. Application should be divided into at least three
layers: Presentation, Business, and Data
2. The Business and Data layers should be common to all
clients.
3. I'm not sure if you currently have multiple versions
of databases (different data models) for each client
version, but there should only be one data model that
matches your one Data layer.  Now usually this creates
some configuration and work to create a data model that
can flexibly support multiple requirements, but you can
usually pull it off.
4. Now for the Presentation layer, without getting into
exactly what you're doing there are two basic choices:
a. (preferred) Create "user groups" or permission groups
for each client that loads a screen list dependent on the
requirements for that client.  Some screens may be the
same for all clients.  Some screens might have run time
configuration differences.  And some screens may only be
accessed by certain clients.  Your application menu loads
the screen list based on the user group the user / client
belongs to.
b. If the requirements are drastically different, you may
want to have a separate presentation layer for each
client.  Not preferred, but much better than creating a
different version for the entire application for each
client

View the Patterns & Practices section of the Microsoft
website for more guidelines.

Hope that helps, I know its general,
Todd