As I mentioned, Hostplus and Australia Super allow you to do this with some caveats, some others likely do too. They allow you to select any stock within the ASX300 and you can buy and sell at your will and pay their equivalent of brokerage, typically around $20 per trade. They limit how much of your portfolio can be in any one stock though and how much of your total portfolio can be invested this way. I don't know exact figures off the top of my head, but it's something along the lines of 60% of your portfolio can be direct investment, and of that no more than 25% can be in any one stock. If a share falls out of the ASX300 it will usually remain in your portfolio, and you can participate in any shareholder benefits, but you cannot buy any more until when/if it returns to the index.
