The homogenous calcitic (?) area in the centre of the picture can be interpreted as a transverse section of a marginal plate of a seastar. The radiate structure beside likely resembles that of a fragmented echinoid spine.
Barnacle sections usually display lamellar structure.
What are the chances for this speciemen to be fragments of a blastoid. In Boardman, Cheetham Fossil Invertebrates, page 582, Figure 18.37, Hydrospire in a blastoid is depicted, which shows some resemblance to upper part of this speciemen, I would be thankful to have your response.