I recently changed my insurance mid way through the year (on lowest deductible so apparently you can change whenever) I applied for 2 supplementary insurances extra and got them no problem (I am not a perfect specimen of health either! - and didn't lie on the forms)

I applied for semi private hospital cover also with the same company before I went with them for basic and supplementary insurances and they declined due to me having to declare a recent operation even though there was a conclusion to the operation and no further treatment needed - I mentioned this to my doc and he called up the insurance company and explained to them in better detail the case surrounding my op, soon after his phonecall to them I got a nice letter from them asking me to re submit my application and they would accept it. After they agreed to this I decided to go with them for all other insurances also.

FYI the insurance company is Concordia

Also I can highly recommend jenny on this forum to help out with insurance matters, she is extremely knowledgeable and helpful and tells you lots of things that you wouldn't normally know about insurance