ss = """
>Entry1.1
704 1   1   1   4
979 2   2   2   0
1220    1   1   1   4
1309    1   1   1   4
1316    1   1   1   4
1372    1   1   1   4
1374    1   1   1   4
1576    1   1   1   4
>Entry2.1
6110    3   1.5 0   2
6129    2   2   2   2
6136    1   1   1   4
6142    3   3   3   2
6143    4   4   4   1
6150    1   1   1   4
6152    1   1   1   4
>Entry3.2
AND SO ON-----------
"""
patbase = """(>Entry *%s(?![^
]+?\\d).+?)(?=>|(?:\\s*\\Z))"""
while True:
    x = input('What entry do you want ? : ')
found = re.findall(patbase % x, ss, re.DOTALL)
if found:
    print('found ==', found)
for each_entry in found:
    print('\n%s\n' % each_entry)
else:
    print('\n ** There is no such an entry **\n')
Извлечение нескольких строк данных между двумя символами — Regex и Python3