I have three different fields representing 3 different things. All can be TRUE, None can be TRUE or only some cane be True.

For instance, I have a picklist for an Account type: Associate, Affiliate, Participants. An Account can be Any ONE of these, or none of these.

I have a checkbox indicating if they are a Licensing Org and another checkbox indicating if they are a Sponosring Org.

An Account can be BOTH a Licensing Org AND a Sponosring Org, but not be an Associate or an Affiliate or a Participant. Or they can be a Licensing Org, but not a Sponosring Org And an Associate, Or they can just be an Associate and not a Licensing Org or a Sponsoring Org. etc.

My initial formula was just looking at my picklist values, but now a wrench was thrown and I somehow need to Account for the other two Checkbox fields.

Any idea how I can do this with a formula?

This was my formula field when I was just looking at the one picklist field. 

CASE(Account.TCH_Membership_Type__c,
"Affiliate Member","Your Company is an Affiliate",
"Associate Member","Your Company is an Associate",
"Participating Member", "Your Company is a Participant",
"", "Your Company is currently not active",
NULL)