A consistency theorem for cardinal sequences of length $<{\omega }_3$

We prove that if $\lambda$ is a fixed uncountable cardinal and $f=⟨{\text{ka}}_{\text{al}}:\text{al}<\delta ⟩$ is a sequence of infinite cardinals where $\delta <{\omega }_3$ and ${\text{ka}}_{\text{al}}\in \{\text{om},\lambda \}$ for each $\text{al}<\delta$ in such a way that $f^{-1}\{\text{om}\}$ is ${\text{om}}_2$-closed in $\delta$, then it is consistent that there is a scattered Boolean space whose cardinal sequence is $f$.