Tags? Classes.
Just data? In Lisp the code, the functions, the symbols, etc. already are data.
Sure one can build another dynamic object system and use fancy names for it. It is really difficult to count the number of times this had been done in the past.
A typical Lisp-based system which does that was Object Lisp:
http://lispm.dyndns.org/docs/ObjectLisp-Manual.pdf
Used by LMI for their user interface and by Coral for Macintosh Common Lisp (until Object Lisp was replaced by CLOS).The idea that a) one can add and remove behaviors (methods) and b) add and remove tags (classes / mixins / ...) at runtime is found in almost every Lisp-based object system. Operations for that are available in every system.
Lisp-based object systems are not that much a language, but more a collection of objects and classes which interact in a defined way. Called a 'system'. That's also we have the Common Lisp Object SYSTEM, and not the Common Lisp Object Language. CLOS is described in terms of objects and their interactions (classes and generic functions are objects themselves) - not so much as a grammar of language constructs.