The fine-grained chronology is arbitrary, because the gospels do not mention time at all.
All four gospels describe the same set of denials; each describes three denials. As an arithmetical possibility there could have been 4 x 3 = 12 denials if we assume that each evangelist describes separate events. However, there is perhaps a slight incompatibility with the second accusation; the rest match completely. So at most there may have been four.
These are the matching aspects:
1. First accusation is from a woman servant. John identifies her further as a “porteress” but that is not a contradiction with the other three accounts.
2. Second accusation involves several people in the audience. That is the common aspect; there are discrepancies of which we’ll talk later.
3. The third accusation comes from a man and happens a while later. The synoptics mention that the accusers noted that Peter is a Galilean; John does not mention that, but it is not a discrepancy.
There are two incompatibilities:
Gender and number of the second accuser(s). Matthew and Mark identify the second accuser as one woman, accusing Peter this time in front of others. Luke has a man as a second accuser, and John says “they” accused Peter the second time. Is this a serious discrepancy? Note that all but Luke agree that a small crowd is present and the accusation is done with them present. So John’s “they” is not really discrepant with Matthew and Mark, as all three describe a small crowd accusing. That Luke identifies the second accuser as a man and does not mention the crowd is still compatible with there being a crowd. I think, John’s “they” is the common denominator, so to say, for the second accusation: it came from several people at once. Luke remembers a man accusing, Matthew and Mark remember a woman pointing to others, and John remembers several, which is probably exactly what happened. In any event, this is not a discrepancy in the number of denials, but in the number and gender of the second accusation.
The second incompatibility is the number of crowings. Only Mark noticed the second crowing and remembers that Jesus also had predicted two crowings. Others speak of one crowing. This does not allow us to separate Mark’s set from the other three because otherwise the three denials match, as we’ve seen. In any event, this is not pointing to separate denials since surely Jesus was not abused first during two crowings and then during a separate crowing.