Generally mixing products together will not provide any extra benefit, but it can be a viable way of getting the benefits from both products simultaneously. This saves time and can often lead to a better look.
But as you’ve also discovered, some products can’t be mixed together. This is because the ingredients in one of the products are either not compatible or they react with the ingredients in the other.
Important Note: DON’T EVER MIX THE FOLLOWING PRODUCTS WITH ANY OTHER PRODUCTS! DOING SO CAN BE DANGEROUS!!
3. Permanent hair colors
4. Semi-permanent hair colors
5. Peroxide (bleach)
The only way to really know if 2 products will be incompatible is to actually mix them together, but here are a few examples that will generally hold true.
Shampoo & Conditioner
These have ingredients that form a salt when mixed together. You’ll still get the shampoo effect but almost no conditioning. This won’t be true of baby shampoos but most others.