The Jacoby Two Notrump convention was a real revolution in its time-- prior to its use, most pairs played 1M - 3M as a forcing raise, and 1M - 2N as natural and forcing. Using 2N as the forcing raise allowed players to make invitational raises with 3M. This doesn't sound like a big deal to those of us who learned bridge in the '80s, '90s, or like me, in the '00s, but it was a huge advance.
But the Jacoby Two Notrump's time was forty years ago. Bidding has evolved so much since then that I think a new set of responses (maybe even a new bid for the forcing raise) is long overdue.
So here's the set of responses I like to play to my partner's 2N:
First step [3C] = any minimum hand
Second step [3D] = non-minimum, no singleton or void
Third step [3H] = non-minimum, a singleton or void somewhere without a good five-card side suit
Fourth step [3S] = non-minimum, a side suit of at least five cards headed by two of the top three honors
Over 3C, partner can relay (bid the next step, 3D), asking for hand-type. Opener responds in the same sort of steps as over 2N - first step [3H] no singleton or void, second step [3S] shortness somewhere, third step [3N] good side suit (this should be rare... when would you treat a 5-5 hand with a source of tricks as minimum?)
Over 3D, cuebids start. 3M is just 'waiting'.
Over 3H, partner can relay with 3S to ask where the shortness is. Opener re-relays with 3N to show a void (partner can ask with a re-re-relay where it is) or can bid their singleton naturally. (If the opening bid was 1H and opener has a stiff spade, opener will rebid 4H.)
Over 3S, partner relays with 3N to ask for the side suit. Opener once again substitutes hearts and spades, as in the last paragraph.
If responder declines to relay, he's showing a cuebid in whichever suit he bids (3N is a substitute cuebid for the relay suit, except, of course, over 3S).
This may seem way too complex written out, but it's fairly easy once you understand the relay and substitution principles in use.
Remember what I said about a new bid for the forcing raise? It seems to work fairly well to use the bid of either 2M+1 or CJS.
2M+1 just means the cheapest bid over a single raise -- 1H - 2S or 1S - 2N.
CJS stands for "cheapest jump-shift"-- 1H - 2S or 1S - 3C. If you use the second scheme, this frees up 1M - 2N as natural and forcing -- so with a hand like Q3 AQJ8 K642 QJ6 over 1S you don't have to bid 2C or 2D on a non-suit, or 2H on a four-card suit.
The advantage of using 2M+1 is that it will keep all of your asking sequences below 4 of your major.
I think overall, using CJS is the better way to go-- but either is better than 1M - 2NT.