On $UP$, $NP$, $\oplus P$ and $PP$?
Consider the oracle machine $N$ that decides $L \in NP^{\oplus P}$. For each computational branch of $N$, if it ends with $\textsf{YES}$, do nothing. If it ends with $\textsf{NO}$, branch and output once $\textsf{YES}$ and once $\textsf{NO}$. Therefore, $L\in  PP^{\oplus P}$.