Unfortunately we don't have a particularly great documentary record when it comes to non-canonical books. That said, there is some clear evidence that at least some people in the early church accepted other "gospels" as Scripture.
Gospel of the Hebrews
Let's first turn to early church historian Eusebius. He divides the existing books into three groups: widely recognized, disputed, and heretical. (Histories, 3.25) His "widely recognized" canon largely agrees with our own, but the "disputed" category is worth noting. These are works that he didn't simply dismiss, but suggests that at least some in the church accepted them. In this list, one in particular can rightly be called a gospel – the Gospel of the Hebrews.
According to the Eerdmans Dictionary of the Bible, among those who knew and used the book are Clement of Alexandria, Origen, Didymus the Blind, Cyril of Jeruslaem and Jerome. And Klijn, "Jewish-Christian Gospel Tradition," argues that Hegesippus accepted it, based on Eusebius's mention of him (Histories, 4.22).
The Gospel of Truth
Perhaps even clearer evidence for the existence of someone holding to more than four gospels in the earliest centuries is found in the writings of Irenaeus. He attacks a prominent gnostic, Valentinus, over the matter:
But those who are from Valentinus, being, on the other hand, altogether reckless, while they put forth their own compositions, boast that they possess more Gospels than there really are. Indeed, they have arrived at such a pitch of audacity, as to entitle their comparatively recent writing “the Gospel of Truth,” though it agrees in nothing with the Gospels of the Apostles, so that they have really no Gospel which is not full of blasphemy. (Against Heresies, 3.11)
Eusebius specifically mentions several more "gospels" in his "heretical" category – the gospels of Peter, Matthias, and Thomas. These and others like them don't have much explicit evidence for their acceptance by some in the church, though presumably Eusebius wouldn't have even mentioned them if no one accepted them. And indeed, their relative prominence is used as evidence for acceptance: see, for example, What is the basis for saying that the Gospel of Thomas was accepted as scripture by early Christians?
So yes, there were people who associated themselves with Christianity – some typically considered "orthodox," some not – who seem to have accepted more than four gospels. Two of the best documented "fifth gospels" are the Gospel of the Hebrews and the Gospel of Truth.