Do Catholics believe in other apparitions like Mary? Or is she unique in this respect?

Do Catholics believe that others saints make apparitions than just Mary?

Traditionally, many of the saints have appeared to various members of the faithful throughout the centuries, as well as Our Lord himself.

At Fatima, Our Lady, St. Joseph and the Child Jesus appeared in the last apparition on October 13, 1917.

St. Catherine of Alexandria, St. Margarite of Antioch and St. Micheal the Archangel appeared to St. Joan of Arc.

St. Joseph appeared at Cotignac, France in 1660. The apparition of St. Joseph at Cotignac is an approved apparion.

According to tradition, Our Lord appeared to St. Peter on the Appian Way in order to encourage him to be crucified for the faith. There is a church built on the site of this apparition, know commonly as the Church of the Domine Quo Vadis.

At Knock, Ireland Our Lady of Knock appeared with St. Joseph and St. John the Evangelist along with Our Lord under the symbolism of the Lamb or God on August 21, 1871.

Now the question may be addressed as if Catholics believe that the apparitions of Mary are in someway unique in some respect?

The answer may be yes or no, depending if we accept St. Joseph’s Assumption as being real or not. Pius tradition within the Church still allows this possibility.

It is not known exactly when the body of St. Joseph was taken up into heaven, but most likely it was soon after Christ's Resurrection or Ascension. Some believe that St. Joseph was among the saints who miraculously rose from the grave as a witness to the resurrection of Jesus, as recounted in St. Matthew's Gospel:

"Many bodies of the saints who had fallen asleep arose; and coming forth out of the tombs after His resurrection, they came into the holy city and appeared to many."

Although it is not an article of the Catholic faith, Pope St. John XXIII made the statement that the assumption of St. Joseph is worthy of belief. Yet, this traditional belief is not widely known or held today. Perhaps St. Joseph's appearance in the sky at Fatima is meant to reignite this belief among the faithful so that we will better understand what a powerful intercessor he is for us, especially for fatherhood, the family, and a model of authentic masculinity, all of which have been so decimated in modern culture.

Now if St. Joseph has been take up into heaven, then Mary’s privilege of having a glorified body and soul is not quite so unique.

It is entirely fitting that the Holy Family, so closely united on earth—both spiritually and physically—is presently united in the same way in heaven.

Francis Suarez maintained St. Joseph was taken up into heaven bodily. St. Bernardino of Siena, Gerson, and St. Vincent Ferrer held the same. St. Francis de Sales points out the fact that nobody claims the tomb of St. Joseph and that there are no relics of this saint. Then he continues in Les Vrais Entretiens Spirituels:

Surely, when Our Lord went down into Limbo, St. Joseph addressed Him in this wise: “Be pleased to remember, Lord, that when you came down from Heaven to earth I received you into my house and family, that I took you into my arms from the moment you were born. Now you are going back to Heaven, take me with you (body and soul). I received you into my family, receive me into yours; I took you in my arms; take me into yours; I looked after you and fed you and guided you during your life on earth; stretch forth your hand and lead me into life everlasting.”

Some have speculated that Saint Joseph was among the “saints” who were resurrected shortly after the death of Christ on Good Friday. - Was Saint Joseph Assumed Bodily into Heaven?

It is thus possible that in addition to Our Lord, both Our Lady and St. Joseph can appear with their glorified bodies to the faithful in an apparition, while other saints can appear in apparitions in the form of a vision!

After all St. Joseph, Our Lady and the Child Jesus all appeared at Fatima on October 13, 1917!

Saints Peter and Paul appeared to St. Thomas Aquinas at night and explained to him a passage he was struggling to interpret in the Book of the Prophet Isaias (Torrell 2010 p. 269).

Do Catholics believe in other apparitions like Mary? Or is she unique in that aspect

Answer

Mary is unique as only Mary possessed a real "glorified body & soul".

The Catholic Church had not approved nor attributed any claimed visions of saints classified as apparition like the Church approved Marian apparitions. Saints had no glorified body unlike the Blessed Virgin Mary. Saints appearances are merely called visions not apparition.

The 4th Dogma of the Assumption stated that Mary was assumed "body & soul". So, in all Church approved Marian apparitions we can be sure that only Mary appeared to visionaries in a glorified body & soul. https://en.wikipedia.org/wiki/Assumption_of_Mary

All the Saints if ever they appeared in a visions is totally different from Mary as the Catholic Church teaches that all the glorified souls of the Saints will only be reunited to their glorified body in Parousia. So, the visions of accounted Saints is far less than the Sovereign Queen of Heaven and Earth as it does not possessed a glorified body.

997 What is "rising"? In death, the separation of the soul from the body, the human body decays and the soul goes to meet God, while awaiting its reunion with its glorified body. God, in his almighty power, will definitively grant incorruptible life to our bodies by reuniting them with our souls, through the power of Jesus' Resurrection.

But the uniqueness of Mary excel even Jesus Christ apparitions, as Mary First Church approved apparition occurred in the year 40AD while She was still very much alive.

Our Lady of the Pillar' the Church called this "Pre-Assumption" apparition. https://en.wikipedia.org/wiki/Our_Lady_of_the_Pillar

Additional Answer

St.Joseph also had an approved major apparitions and this would mean that the homily of St.John XXIIII stating the merit of the resurrection of St.Joseph body was true. St.Joseph body was resurrected meaning when St.Joseph appeared in a visions what were seeing is a glorified body and soul like Mary and Jesus.

On May 26, 1960 Pope John XXIII in his homily for the feast of the Ascension of Our Lord made a statement that the Assumption to Saint Joseph is worthy of pious belief (). He also stated that he believed the same privilege was accorded to Saint John the Baptist33. This is the first time that a Pope has ever made a public statement on the subject and the fact should offer great reassurance to those who feel it would be contrary to their religious sentiments to imagine Christ refusing Joseph this crowning grace. Pope John's words are a guarantee that such a belief is truly prudent and therefore can no longer be classified as a "pious exaggeration". https://www.ewtn.com/library/MARY/THEOINTR.HTM

Here's the link on the Church approved apparitions of St.Joseph;

Devotion To St Joseph’s Most Chaste Heart – Approved Apparitions…

Many know about approved apparitions of our Blessed Mother. But only a handful realize that there were apparitions in Itapiranga, Brazil from 1994-1998 in which St. Joseph appeared along with Mary and Jesus.

In January 2010, after much study, prayer, reflection, observation and seeing the growth in the faith life of thousands, the local ordinary, Bishop Carillo Gritti declared a Decree of Worship favoring the Itapiranga appearances and in an earlier document called it of “supernatural origin.” https://catholictruthblog.com/2016/08/09/devotion-to-st-josephs-most-chaste-heart-approved-apparitions/

So, the Catholic Church devotion to the Holy Family is now complete. The Sacred Heart of Jesus, the Sorrowful & Immaculate Heart of Mary and also the Devotion to the Chaste Heart of St.Joseph.