TL;DR version: hand code your search templates.
In more detail I’d note firstly that generally user aren’t encouraged to use large numbers of terms for queries as it tends to slow response time. If you find yourself needing 8 or 9 search terms likely it’s your data telling you it needs some better curating and some extra metadata. That said…
Yes, it’s perfectly possible to have more than 5 input terms. BUT, you can’t configure such search templates via the the NP Assistant publishing wizard; it’s hard-coded to only allow 5 choices. So, you need to hand code the templates. That means editing the NPT files and reading the NP API which is part of Portfolio Server Admin Guide since v9. The NP API hasn’t changed** between launch (alongside v7) and v10, though the latter only adds to existing functionality and doesn’t change existing stuff.
By way of expectation management, NP queries are parsed in left to right (i.e. top to bottom as written in a page’s code). also, nested queries such as are common in SQL are not supported***. You can do (A or B) and (C or D), NP will interpret that as (((A or B) and C) or D).
** Indeed, the original typos still survive including some code-breaking case-sensitive errors. So, expect some misdirection from the API doc. Corrections have been submitted, but never seem to get applied even when other parts of the manual are updated.
*** Enterprise users with SQL catalogues can write custom PHP?ASP pages directly querying the catalogue though of course that bypasses NP.