If you are fourth seat after a third seat raise, can you make a takeout double with "intermediate" values?
This is a matter of partnership agreement!

The disadvantage of agreeing that you can jump in with 11hcp and a singleton is that opener could have a quite strong hand, and doubling gives opener the option of passing with it.  This gives opponents the option of doubling your partner, and they also gain information that is useful in the play.  Another disadvantage is that your partner knows less about your hand when you double.  (This is particularly disadvantageous when opener re-raises to 3 (note most experienced partnerships will play this as a minimum LOTT bid after the double, since they have a redouble/2N as well as help-suit/strong-suit/short-suit tries to invite with) and partner needs to decide whether to compete further.)

The advantage of agreeing that you can balance with 11hcp and a singleton is that, when you pass and opener passes, your partner now has less pressure to reopen with a marginal hand, because they know more about how unsuitable for competition your hand is.  Also, you have a slightly better chance in finding those 22hcp distributional games in the other major.  Agreeing to double weaker helps you find the game with the 11-11 split in your hcp at the cost of making it harder with the 14-8 split, and the 11-11 split is more likely.

There is a similar question when it comes to how strong you need to be to make a takeout double of a weak 2.  Some play that you can do it on about the same strength as a takeout double of an opening 1 bid, and others play you need a point or two extra.  Again you trade the ability to give more information to partner when you do double with the ability to give more information to partner when you don't double.

To some extent, this decision depends on whether you are willing to play Lebensohl (or some other convention achieving similar purposes) or not.  It may make sense to have different agreements over 2H than 2S, but most partnerships are probably not willing to have that memory load on their system.

It also depends on form of scoring and vulnerability, since getting to -100 (for say 3DX-1 nonvul) rather than -110 (for 2S+2 their way) is much more important at MPs than at IMPs.  (But it depends on form of scoring less than you might think, because conversely getting to +110 (for 3D+3) rather than -110 is worth much a lot more at IMPs than MPs.)