Actually, no he doesn't. The pope can't CHANGE established doctrine. For example, he can't add a fourth person to the Holy Trinity.
The Pope can change Catholic doctrine, just not all at once. He and his priests have to do it brick by brick, and it can take decades or centuries, but it happens. I believe either Mary’s “Immaculate Conception” or her “perpetual virginity” was established this way (or quite possibly both). First introduce the idea as possibility, speculate on it, and then many years later when people have grown used to the idea (that is, it’s taken root), then declare it dogma.
On a “fourth person of the Holy Trinity,” back in 2006 I was fairly new in really knowing the Lord, which came mostly from reading the whole Bible, and I was open to anything that seemed to come from Bible-believing Christians. So I watched EWTN for a few years. And at the close of one program, a host actually referred to “the mother, the Father, the Son and the Holy Spirit” (possibly ordered the Father before mother, though.”) I don’t remember anything else but it being said (and I heard it again in a repeat presentation so I know for sure it was said) . I just wasn’t wary of the Catholic Church, then, so I noted it with disapproval but didn’t consider it deeply like I started to after some years of encountering disturbing things coming out of the Catholic Church.
The pope can. He did so in 1870 and 1950. Check it out.