Yes, you can embed multiple Clipchamp buttons on a website or page. When clicked, each button will launch a separate instance of the Clipchamp API including its JS webcam input option if this is one of the input options you selected, however they will not work at the same time, only in sequence.
For instance, this is useful in cases where you're asking your website visitors to answer a number of questions and would like them to record a new video for each answer - as some of our API customers do.
Each of their answers will then get uploaded as a separate video file to your cloud storage.
You can do this through the Clipchamp API or if you're on WordPress, by using our plugin and simply embedding more than one [clipchamp] shortcode on a page or post.