No, there are no restrictions on the number of universities where you can apply for early entry schemes. However, there may be restrictions on the type and number of degrees that you can apply for, depending on the university. Examples of such restrictions include:
- A maximum number of degrees that you can apply for under an early entry scheme. Examples include UNSW's Gateway Admission Pathway, WSU's HSC True Reward Early Offer Program and MQ's Leaders and Achievers Early Entry Scheme.
- Degrees excluded from early entry schemes. In the case of WSU, there is a list of excluded degrees, some of which may be subject to additional selection criteria and capped placements, such as the Doctor of Medicine. Another example is MQ's Leaders and Achievers Early Entry Scheme, which excludes the Bachelor of Actuarial Studies/Bachelor of Professional Practice (Honours) (Co-op).
There may be other criteria that must be met, which are typically associated with converting a conditional offer into an unconditional one (SRS is relevant here). Such criteria can include placing the eligible degree(s) as your first preference by a certain date, successfully completing the HSC, achieving a specified minimum ATAR as well as meeting any additional institution and/or degree-specific requirements.
I hope this helps!