Short answer, no.
The cover letter is almost exclusively meant to very quickly set the tone and prepare readers to “see” specific details about your experience when they move on to the resume. In almost all cases, this is most effectively accomplished with a one-page cover letter (essentially half a page when you account for addresses, etc.).
In all of my years developing job search documents for clients, I can count on one hand the number of cover letters I’ve written that extended beyond one-page. Those rare instances were for very specific positions that expressly requested a more comprehensive cover letter.
When creating your cover letter, respect readers’ time and the intent of the letter by keeping it concise and powerful.