Here is an example of a program that uses nested conditional statements. Click the mouse when touching each sprite and when not touching each sprite. What differences do you notice? The code stacks for the dog and cat sprites use the same blocks. The difference is the sequence (which conditional statement is nested).
You can check out my video tutorial for Conditional Statements on the official Scratch YouTube channel (look for the Conditional Statements video series) and find a link to written resources related to this topic in the video description.