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Firmly continuationist, it shouldn't surprise that LDS appear here.
Multiple modern-day Christophanies recorded in Doctrine & Covenants and The Pearl of Great Price.
There is explicit doctrine that Jesus can and does appear to people (D&C 130:3)
Other personal appearances where there is recorded testimony:
Note: LDS believe the Second Coming is still in the future, none of these appearances should be confused with the Second Coming.
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Which Christian groups or denominations believe in modern-day Christophanies?
Both Catholicism, Eastern Orthodoxy and the Church of Jesus Christ of Latter-Day Saints claim to have Christophanies.
A Christophany being an appearance or non-physical manifestation of Christ. Traditionally the term refers to visions of Christ after his ascension, such as the bright light of the conversion of Paul the Apostle.
According to Wikipedia, the following Christophanies have occurred:
Saint Jerome is believed to have had a precise vision of the Trinity, as is illustrated by Andrea del Castagno.
Magdalena de Pazzi was a mystic who claimed several Christophanies about the Trinity.
LΓΊcia dos Santos of Fatima claimed to have seen Jesus in the Trinity in Tui in 1926.
Mary Faustina Kowalska claimed to have had recorded her visions of Jesus.
Joseph Smith claimed to have seen both Jesus Christ and God the Father in an event known as the First Vision.
The visions of Christ to St. Faustina Kowalska are the most well known Christophanies of the modern day times. I am sure more exist.