Agree with JackquiD. In writing, "that" will only modify a thing and "who" will only modify a person. Just remember that in conversation people will often use "that" to modify a person too.
Usually an attributive clause modifies the noun that comes directly before it. In this sentence there is a prepositoinal phrase ("with our customers and suppliers") and so it is a bit confusing.
Honestly, the rule here is you have to figure it out based on the context. It doesn't really make sense to say that "customers and suppliers" are "a radical departure," therefore the clause is modifying "new business relationships."