If you mean a normal user which application-wise is granted
higher privileges by ACLs, you need to make use of the granular
"a" (add) and "z" (zap) privileges (their union is "w", write).
Pardon my thickness, but the documentation at http://www.openldap.org/doc/admin24/access-control.html specifically calls out the possible values of the "level" part of the ACL clause:
<level> ::= none | disclose | auth | compare | search | read | write | manage
Is this an undocumented feature? Should perhaps the documentation be updated, or maybe an example of this sort of ACL included in the examples section?