There is no limit to the amount of government grants you may apply to for starting a new small business in Australia, barring ineligibility. Not every Australia grants applicants are going to be approved for what they need for starting a new small business, for one reason or another. So, do what you can to make yourself the best prepared, best informed applicant there is and do not hesitate to apply for multiple grants to increase the chance you will be approved for at least one.
You can also take advantage of the Small Business Startup Assessment Tool below and see the tools and resources you need to succeed at launching your business. It takes just a minute and will also tell you if there may be any funding programs available.