According to John's Gospel, there were at least three Passovers during Jesus' ministry. We should not assume there were only three. All four Gospels report on Jesus' last Passover. Other major events in all four accounts include Jesus' Baptism, John the Baptist's arrest, the Baptist's beheading, and the feeding of the 5,000.
The Baptist's arrest comes shortly after Jesus' first public Passover. The beheading is reported just before he feeds the 5,000, which corresponds with the middle Passover of the fourth Gospel. Events before and after that Passover differ dramatically. John's death changed things for Jesus in major ways.
No two Gospel writers report the same Episode (events, not pericopes) in two different 'halves' of Jesus' ministry. Events sequenced differently by Matthew or Luke as compared with Mark occur exclusively in the period before John's death, in all three Synoptic Gospels. Events from John's death through Palm Sunday never differ in sequence among the Synoptics.
Chronologies of the Gospels basically differ in how they treat the two 'halves' of Jesus' ministry. Restricted by a few key dates, events from the Baptism to John's death must cover either one or two years, plus a few months. Likewise, events from John's death to Palm Sunday span either two or three total Passover (thus covering precisely one or two years). Chronologists of the Gospels normally disagree most in how they 'read' the 'clues' to arrive at a two, three or four year conclusion.
However, to combine a high view of scripture with a historical view of scripture's reported events, there are better ways to proceed than by exegesis alone.
Chronological study does not depend exclusively on chronological indicators found in a text. Travel time, Sabbath days, the festival schedule, contemporary historical events, and natural logistical limitations all come into play. Events themselves require significant amounts of time in which to occur. Additional space to allow for non-recorded events also must be considered. By any historical analysis (assuming reliability of information), the testimony of the Gospels contains less than everything that happened, but more than enough to reconstruct one plausible timeline of events which best accounts for all the evidence.
The two year chronology of Jesus' public ministry is positivist minimalism that requires the Lord to move constantly at a breakneck pace for most of that 24 months. It also speeds up political developments and the spread of news across various regions. Such a timeline is unrealistic because of the sheer amount of travel and activity accounted for in the Gospels as a whole, not to mention the intense personal, interpersonal and psychological needs and concerns of the major players. Furthermore, such efficiency with the data is not generally the outcome of a properly historical analysis.
We must remember, it is at least as likely that John has left out one or two Passovers. For this reason, the most thorough chronological studies of the Gospels usually posit three or four years for Jesus' ministry, from the Lord's first public Passover to his last. The question of that final difference (3 or 4 years) depends on events between John's death and Palm Sunday. We may or may not have arguable clues in Matthew's two-drachma tax and the parable of the fig tree's mercy year (see Cheney). Far better than 'clues', however, is history itself.
The 3 year view is more popular because it's traditional arguments include entrenched apologetic defenses for inerrancy. However, the 4 year view is more likely, for two reasons. First, both halves of Jesus' ministry fit better in two years than in one. Second, Roman History shows the overall sequence of events fits better from 29 to 33 than it does from 30 to 33. (By the way, none of it fits before 30 AD, although many neglect fleshing things out well enough to realize this.)
In the final analysis, it is the reconstructed chronology itself that elucidates the disputable 'clues' in the Gospels and reveals far more chronological reliability to each Gospel Testimony than could ever be fairly granted by an analysis of their own 'plain sense' alone.
There are several posts on this site supporting the four year chronology of Jesus' ministry.
There will be - no doubt - many more to come.