Large auto-transformers are provided with a tertiary winding .Unless specifically called for ,such stabilising windings will have a rating much less than 331/3% ,percentage that is normally provided for two winding transformers.
Normally such tertiaries are loaed with reactors or capacitors and customer normally specify the load and power factor for such loads .Then manufacturer can design the unit for ,say 100/100/30 MVA load ie you can load both secondary and tertiary for full rating with out primary getting overloaded.Then temperature rise test also will be done for 100/100/30 MVA loading.
But if the tertiary is used for a consumer load of say 30 MVA ,then the rating of the secondary shall be adjusted such that the primary is not overloaded ie secondary load will be reduced to that extent.Normally tertiary impedance will be low and any fault on terminals will cause heavy currents in auto-transformer .So normally in such cases users specify specially high impedances for tertiary or put a reactor in series.In USA one utility which was using tertiary for station loading was putting the trf on the main auto itself,ie "piggy riding"on main unit so that chances of a 3L fault on tertiary terminals are avoided.
Greatest disadvatantage as mentioned by previous contributors is the disturbance to your main power flow due to line faults on your tertiary distribution circuit.Many times this will be counterproductive.I remember a case when a utility was planning to use the tertiary of a 1500 MVA auto bank for loading station load of 5-10 MVA. I could convince the utility the futility of such a provision as any fault in the tertiary circuit will affect his 1500 MVA power flow.It may be better to put a separate MV line for such loadings rather than piggy ride on your critical large capacity auto transformer.