Extensions of deformed $W$-algebras via $qq$-characters

We use combinatorics of $qq$-characters to study extensions of deformed $W$-algebras. We describe additional currents and part of the relations in the cases of $\mathfrak{g}\mathfrak{l}(n\mathrm{\mid }m)$ and $\mathfrak{o}\mathfrak{s}\mathfrak{p}(2\mathrm{\mid }2n)$.