Negative Continuations over 1

After a 1 response to 1, showing 0-7 HCP, opener chooses from the following bids.

1 is artificial and forcing, showing at least 20 HCP
1NT shows 16-19 and a balanced hand. Strong NT systems are on (Stayman, Transfers, whatever you usually play over a strong 1NT opening)
Other cheapest suit bids are natural (5⁺), show 16-19 points, and are invitational. Further bidding is natural.
Jump bids in a suit are also natural and show 16-19 points, but are more distributional and make stronger invites. Further bidding is natural.

Following 1-1-1, a bid of 1 is a 2^nd negative, showing 0-4 HCP (and, according to some, not a 4-point hand with an ace). Other bids show 5-7 points. The next 4 bids (1NT through 2) are transfers to 5-card suits, and 2 shows a balanced hand. If opener accepts the 2 relay to 2NT, responder bids like Stayman.

After 1-1-1-1, responder can bid the following:

1NT is natural, showing 20-22 points and a balanced hand. Strong NT systems are on. Yes, there is little point in a "transfer" since all suits have been bid, but this way we avoid learning yet more systems.
2 is artificial and forcing, showing 23 or more HCP.
Other bids are the same as after 1-1, but stronger.

After 1-1-1-1-2, showing 23⁺ HCP, 2 by responder is a 3rd negative (0-2) and you can use whatever methods you like as in a standard 2-2 opening, given that responder is nearly broke. Our methods are that any rebid by opener is natural and everything except 2NT (or game) is forcing. Other bids by responder are transfers showing 3-4 HCP and a 5-card suit (2 is again balanced).