We consider the problem of computing \(\ell \) -page queue layouts, which are linear arrangements of vertices accompanied with an assignment of the edges to pages from one to \(\ell \) that avoid the nesting of edges on any of the pages. Inspired by previous work in the extension of stack layouts, here we consider the setting of extending a partial \(\ell \) -page queue layout into a complete one and primarily analyze the problem through the refined lens of parameterized complexity. We obtain novel algorithms and lower bounds which provide a detailed picture of the problem’s complexity under various measures of incompleteness, and identify surprising distinctions between queue and stack layouts in the extension setting.