Functional Analysis – Continuous fields of C * algebras of dimension one in a dense set

At a Hausdorff on-site compact space $ X $Consider a continuous field $ {A_x } _ {x in X} $ by C * -Algebren over $ X $, so that $ A_x $ is one-dimensional for everyone $ x $ in a dense subset $ D $ from $ X $while the dimension of $ A_x $ is greater than one for $ x $ in the $ X setminus D $, I can put together some simple examples $ X setminus D $ is a discrete sentence, but I wonder how much more complicated this can be. I would like to know:

Is it possible to build an example of this? $ D $ can not be open.