Prevent non-greedy part from consuming the following optional part

I have a regex with a mandatory part, a non-greedy (lazy?) part, an optional part and finally another non-greedy part.

<mandatory><non-greedy><optional><non-greedy>
Implemented as:
^mandatory.*?(:?optionalpart)?.*?$

The optionalpart consists of 'a piece to find' and 'a piece to return in a capture group'.

^mandatory.*?(:?findme(matchme))?.*?$

But for some inputs the first non-greedy part consumes characters that the following optional part should match. Is there a way to make the optional part more greedy than the previous non-greedy part?

Example: Find the character after the 2,, or find an empty string if there is no 2, but the mandatory part matches.

"Foo: 2,b,1,a,3,c" -> match, $1 = "b"
"Foo: 1,a,2,b,3,c" -> match, $1 = "b"
"Foo: 1,a,3,c,2,b" -> match, $1 = "b"
"Foo: 2,b"         -> match, $1 = "b"
"Foo: 1,a,3,c"     -> match, $1 = ""
"Fuu: 1,a,2,b,3,c" -> no match.

Attempt 1: ^Foo: .*?(?:2,([a-z]))?.*?$
This fails on the 2nd and 3rd example, returning "" instead of "2".

Attempt 2: ^Foo: .*?(?:2,([a-z])).*?$
This fixes the previous fails, but now fails on the 5th example, not matching.
The part that must be optional is no longer optional.

_{If it matters, I'm using Java's Pattern class.}

This was asked before, but there was no satisfactory answer for either of us.

Solution

Your first regex is very close, you need to move (?: a bit more to the left to include the .*? pattern:

^Foo:(?: .*?2,([a-z]))?.*$
     ^^^

See the regex demo

Details

^ - start of string
Foo: - some literal text
(?: .*?2,([a-z]))? - an optional non-capturing group that matches greedily (will be tried at least once) 1 or 0 occurrences of:
- .*? - space followed with any 0+ chars other than line break chars, as few as possible
- 2, - a literal substring
- ([a-z]) - Group 1: a lowercase letter
.* - any 0+ chars other than line break chars (the rest of the string)
$ - end of string.

The general pattern will look like

^<MANADATORY_LITERAL>(?:<NON_GREEDY_DOT>(<OPTIONAL_PART>))?<GREEDY_DOT>$