I came up with this solution using a map. The main problem I had was exceeding the $1-$9 limitation on placeholders.
RewriteMap filtermap txt:content/maps/filtermap.txt [NC]
RewriteCond ${filtermap:$6|NOT_FOUND} !NOT_FOUND [NC]
RewriteRule ^models/([^/]*/[^/]*)/([^/]*/[^/]*)/([^/]*/[^/]*)/([^/]*/[^/]*)/([^/]*/[^/]*)/([^/]*/[^/]*) /models/?${filtermap:$1}&${filtermap:$2}&${filtermap:$3}&${filtermap:$4}&${filtermap:$5}&${filtermap:$6} [NC,L]
RewriteCond ${filtermap:$5|NOT_FOUND} !NOT_FOUND [NC]
RewriteRule ^models/([^/]*/[^/]*)/([^/]*/[^/]*)/([^/]*/[^/]*)/([^/]*/[^/]*)/([^/]*/[^/]*) /models/?${filtermap:$1}&${filtermap:$2}&${filtermap:$3}&${filtermap:$4}&${filtermap:$5} [NC,L]
RewriteCond ${filtermap:$4|NOT_FOUND} !NOT_FOUND [NC]
RewriteRule ^models/([^/]*/[^/]*)/([^/]*/[^/]*)/([^/]*/[^/]*)/([^/]*/[^/]*) /models/?${filtermap:$1}&${filtermap:$2}&${filtermap:$3}&${filtermap:$4} [NC,L]
RewriteCond ${filtermap:$3|NOT_FOUND} !NOT_FOUND [NC]
RewriteRule ^models/([^/]*/[^/]*)/([^/]*/[^/]*)/([^/]*/[^/]*) /models/?${filtermap:$1}&${filtermap:$2}&${filtermap:$3} [NC,L]
RewriteCond ${filtermap:$2|NOT_FOUND} !NOT_FOUND [NC]
RewriteRule ^models/([^/]*/[^/]*)/([^/]*/[^/]*) /models/?${filtermap:$1}&${filtermap:$2} [NC,L]
RewriteCond ${filtermap:$1|NOT_FOUND} !NOT_FOUND [NC]
RewriteRule ^models/([^/]*/[^/]*) /models/?${filtermap:$1} [NC,L]
Its not super pretty but it does work. The filter map looks like this
p1/v1 p1=v1
p2/v2 p2=v2
...
This is not an ideal solution if your combinations of p1/v1 are unlimited, but mine are finite so its pretty easy to manage.