We　propose　a　scheme　for　the　generation　of　highly　excited　Dicke　states　for　multiple　atoms.　In　the　scheme　N　+　1　atoms　dispersively　interact　with　a　vacuum　cavity,　with　the　last　atom　having　a　different　coupling　and　driven　by　a　classical　field.　As　the　first　N　atoms　are　symmetric,　they　remain　in　the　symmetric　Dicke　subspace,　with　the　spacing　of　energy　levels　being　unequal　due　to　the　vacuum　light　shift.　Employing　the　Stark　shift　induced　by　the　classical　field,　one　can　tune　the　last　atom　in　resonance　with　the　transition　between　two　specific　Dicke　states　of　the　first　N　atoms.　So　the　detection　of　the　state　of　the　last　atom　conditionally　collapses　the　first　N　atoms　to　the　desired　Dicke　state.