The capacity of private information retrieval (PIR) from databases coded using maximum distance separable (MDS) codes was previously characterized by Banawan and Ulukus, where it was assumed that the messages are encoded and stored separably in the databases. This assumption was also usually made in other related works in the literature, and this capacity is usually referred to as the MDS-PIR capacity colloquially. In this work, we considered the question of if and when this capacity barrier can be broken through joint encoding and storing of the messages. Our main results are two classes of novel code constructions, which allow joint encoding, as well as the corresponding PIR protocols, which indeed outperformed the separate MDS-coded systems. Moreover, we show that a simple, but novel expansion technique allows us to generalize these two classes of codes, resulting in a wider range of the cases where this capacity barrier can be broken.