A most naive generalization of the Gauss hypergeometric equation would be an equation $H_3$ of order three with three singular points, which has one accessory parameter.
An `addition and middle convolution' takes $H_3$ to an equation $H_6$ of order six with three singular points and one accessory parameter.
We study shift operators and symmetry of $H_6$ and get a restriction $E_6$ of $H_6$, where the accessory parameter is a cubic polynomials of the local exponents.
An `addition and middle convolution' takes $E_6$ to a restriction $E_3$ of $H_3$. The Dotsenko-Fateev $SE_3$ equation is a special case of $E_3$.
We study shift operators and special solutions of $SE_3$.