You can use a non-regex approach here with Split and Skip:

var text = "ABC_BC_BE08_C1000004_0124";
var result = text.Split('_').Skip(2);
foreach (var s in result)
    Console.WriteLine(s);

Output:

BE08
C1000004
0124

See the C# demo.

With regex, you can use

var result = Regex.Matches(text, @"(?<=^(?:[^_]*_){2,})[^_]+").Cast<Match>().Select(x => x.Value);

See the regex demo and the C# demo. The regex matches

• (?<=^(?:[^_]*_){2,}) - a positive lookbehind that matches a location that matches the following patterns immediately to the left of the current location:
  • ^ - start of string
  • (?:[^_]*_){2,} - two or more ({2,}) sequences of any zero or more chars other than _ ([^_]*) and then a _ char
• [^_]+ - one or more chars other than _

Usign .NET there is also a captures collection that you might use with a regex and a repeated catpure group.

^[^_]*_[^_]*(?:_([^_]+))+

The pattern matches:

• ^ Start of string
• [^_]*_[^_]* Match any char except an _, match _ and again any char except _
• (?: Non capture group
  • _([^_]+) Match _ and capture 1 or more times any char except _ in group 1
• )+ Close the non capture group and repeat 1 or more times

.NET regex demo | C# demo

For example:

var pattern = @"^[^_]*_[^_]*(?:_([^_]+))+";
var str = "ABC_BC_BE08_C1000004_0124";
var strings = Regex.Match(str, pattern).Groups[1].Captures.Select(c => c.Value);

foreach (String s in strings)
{
    Console.WriteLine(s);
}

Output

BE08
C1000004
0124

If you want to match only word characters in between the underscores, another option for a pattern could be using a negated character class [^\W_] excluding the underscore from the word characters in between:

^[^\W_]*_[^\W_]*(?:_([^\W_]+))+