Editing website HTML and intercepting any responses

My college has some web software that is absolutely horrific and I want to redesign it locally to save my eyes. Obviously I could use developer tools but that gets overwritten on a reload, but I was wondering if it's possible to edit something in the developer tools (like remove a div) and to then 'save' it as to intercept any response from the server and rewrite it using the HTML I have 'saved'