There is an old debate about whether a new suit by responder (e.g. 1S : (2C) : 2H) should be forcing or not. Either method is very useful when the appropriate hand type comes up - and causes difficult problems when you pick up a hand of the opposite type. If forced to choose one or the other throughout, I would prefer to play a new suit as forcing (which is standard in most parts of the world). Though non-forcing free bids do look very attractive when the suit is a major that can be shown at the 2-level.
But there is no need to choose. By using artificial tricks such as transfers we can usually show both hand types at an appropriate level. Unfortunately, different situations require different gadgets. Below are the methods I'm currently using for 2-level interference over 1D/1H/1S openings, which demonstrate all the various ideas that might be used.
1. Over a 2C overcall.
Here we use switch: that is, of the two unbid suits, a bid in one of them shows length in the other one. So:
Over 1D : (2C), 2H shows spades and 2S shows hearts.
Over 1H : (2C), 2D shows spades and 2S shows diamonds.
Over 1S : (2C), 2D shows hearts and 2H shows diamonds.
This essentially gives us both a forcing and a non-forcing bid in the higher-ranking suit, while not raising the level on the lower-ranking suit.
Note that the "switch" relies on both unbid suits being at the same level. So if you are fond of this method you could use it over spade overcalls as well, and also over 1S : (2H) and suchlike. But we actually do different things there.
2. Over 1M : (2D)
Here we free up some space by giving 2NT an artificial meaning. This allows for the following structure:
A bid of 2 of the other major is natural and not forcing.
2NT shows clubs.
3C shows the other major (stronger than the NFB).
3. Over 1D : (2M)
Again it makes sense to use 2NT as a transfer to clubs here. Unfortunately this time there is a real shortage of space, since while we would like to use 3C to show the other major, it would also be nice to have a way to show a good diamond raise below 3D. We can't realistically do both.
I currently play 3C as the diamond raise, so over 1D : (2S) we have to play 3H the traditional way, natural and forcing. Over 1D : (2H) we have 2S as a NFB and 3H showing a stronger hand with spades.
4. Over 1M : (2OM)
This is where transfers really come into their own. Again starting from 2NT we can play
2NT shows clubs
3C shows diamonds
3D is a raise. (When we have two artificial raises available below 3M, as with 1S : (2H) : 3D/3H, we use them to distinguish between 3- and 4-card support.)
Exactly the same transfers work if opponents bid 2M Michaels over our 1M opening.