Yes, you can do this with Child Themes. A child theme is a WordPress theme that is based on another theme. The child theme points to the parent theme, and inherits styles, functions, and templates from the parent theme. However, in the child theme you can override any style rules and templates that you want with new ones.
Depending on how extensive the changes you want to make are, you might create a child theme that includes just a few style sheet changes, inheriting everything else from the parent. If you want to make more changes, you can include new templates to replace the old ones.
The big advantage you have creating a child theme (rather than simply editing the existing theme) is that in the future when the original theme developer issues an update to the parent theme, you can update the parent theme and you won’t lose any changes that you made with your child theme.