Most frequent integer in a list
You could use itertools.takewhile to keep on taking tuples until they are not the same count anymore:

from collections import Counter
from itertools import takewhile

def integer_frequency(integers):
    int_freq = Counter(integers)
    most_common = int_freq.most_common(1)[0]
    return list(takewhile(lambda x: x[1] == most_common[1],
                          int_freq.most_common()))


I also renamed your integer_list to integers, because it can be any iterable of integers.

Alternatively, you could use itertools.groupby to group the tuples by their frequency and return the group with the highest frequency, as @Gareth Reese has suggested in the comments:

from collections import Counter
from itertools import groupby

def integer_frequency(integers):
    return list(next(groupby(Counter(integers).most_common(),
                             key=lambda x: x[1]))[1])


This approach is consistently faster (by a small amount):



However, both beat your algorithm by quite a lot: