Stacking Discounts on a Single Discount Code

We have existing volume discounts at different pricing tiers set up, and these are working properly through the app, but we are also trying to add a rule that would give a free product when the cart total is over $30.
So for example we have the following volume discounts:

5% off $25 or more.
10% off $50 or more.
15% off $75 or more.
20% off $100 or more.

I understand that we can't apply two completely separate discount codes at checkout, so if we have two different codes for the free product over $30 and the volume discounts this won't work.
What I'd like to do (since I can't stack multiple discounts):

5% off $25 or more.
5% off + Free Product at $30 or more
10% off + Free Product at $50 or more
15% off + Free Product at $75 or more
20% off + Free Product at $100 or more

Is this possible?