# On lowness of $\oplus P$

$\oplus P$ is low for itself ($\oplus P^{\oplus P}=\oplus P$).

1. Are there other complexity classes $\mathcal D$ that satisfy $\mathcal D^{\oplus P}=\oplus P$?

2. Are there complexity classes $\mathcal C$ that satisfy $\mathcal C^{\oplus P}=\mathcal C$?

Weak complexity classes will satisfy $\mathcal{D}^{\oplus P} = \oplus P$. For example, $P^{\oplus P} = \oplus P$.
Strong complexity classes will satisfy $\mathcal{C}^{\oplus P} = \mathcal{C}$. For example, $\mathsf{PSPACE}^{\oplus P} = \mathsf{PSPACE}$.