IME, DXM can definitely be that kind of drug, if its approached properly. DXM is definitely one of my favorite entheogens, and has a lot of potential to provide an enlightening, thought-provoking or mystical experience. Ive taken DXM approx. 20 times, both in recreational and spiritual doses and settings, and I've discovered that one of the best ways to approach it is to start off with a particular idea or 'theme' in mind, which will then be the focus of your experience. Since DXM has many unique qualities which include deriving much of the tone of your experience from the past activities of your day, it can be helpful to spend the day prior to your experience focusing on whatever subject you want to explore in your experience. Then, dose later in the day (night is best for DXM) and attempt to meditate as you become aware of the action of the chemical. Ideally, you're music selection and environment should reflect the theme of your experience to some degree, or at least be neutral enough so that it will not clash with you're mindset. DXM is a very "complicated" psychoactive IMO, however, so you may want to have an experience with a medium dose of something like LSA containing Morning Glory or Hawaiian Baby Woodrose seeds, or, if you're feeling very brave, something like cohoba snuff.
With any psychedelic though, the two most important ways to ensure a deep and meaningful experience is preparation ahead of time (spontaneous trips can be just as meaningful, but much more unpredictable) and to accept your experience for what it is, and neither try to control it or fight against it. Simply let it overtake you, and draw whatever conclusions you wish from the experience, rather than imposing them on it from the start.
By the way, feel free PM me if you have any other specific questions about DXM, as its quite an interest of mine and Ive had a good deal of experience with it.