Hero Augment Rules

Does anyone know how hero augment rules work? If this knowledge is posted somewhere else please share! I want to be more informed when deciding how to pick/reroll hero augments. Here is my basic understanding of how the game offers you hero augments:

- Stage 2 can offer any combination of 1 or 2 cost hero augments (1-1-2, 1-2-2, 1-1-1, etc). This is pure random in the sense that none of these offerings are influenced by your current board state.

- Stage 3 can offer any combination of 2 or 3 cost hero augments (2-2-3, 2-3-3, 2-2-2, etc). These offerings can be influenced by your current board state.

- Stage 4 can offer any combination of 3, 4, or 5 cost hero augments (3-3-4, 3-4-4, 4-4-5, etc). These offerings can be influenced by your current board state.

- Threat hero augments can be offered at any time in stage 3 or 4. They are not offered in stage 2 because there are no 1 or 2 cost Threats. - Stage 3 and 4 hero augment offerings can be influenced by your current board state based on any active traits on your board

Am I missing anything here? Is my understanding of these rules just wrong?