The simple answer is yes you can be carrying on a business of share trading and also be an investor in respect of certain CGT assets . However, whether certain CGT assets are trading stock or investments is far from a simple matter.
Whether your circumstances fit within the "criteria" to be able to do so is another question.
A key factor is your intention in respect of the relevant CGT asset at the time of acquiring it and proving that the relevant CGT asset wasn't held as part of that business of 'share trading'. The ATO's default position is likely to be that everything is part of the trading business and it is up to you to be able to prove otherwise.
Of course the above is an oversimplification of the issues and considerations that need to be taken into account so you really should consult with a registered tax agent.
