A lot of partnerships play that a 2D response to a strong 2C is waiting but positive. If so, with a very weak hand, responder will bid 2H which some play shows no ace or king while others play that it shows at most three jacks or one queen. Has your partnership discussed what means what after that?  Here is a suggested structure for suit rebids and responses after a negative 2H response to a strong 2C.

• 2C-2H (Double Negative)
• 3H = One-suited heart hand (passable, bid 4H if you want to be in game)
• 2S forcing 2NT followed by 3S = One-suited spade hand (passable, bid 4S to always be in game)
• 2S forcing 2NT followed by 3C or 3D = Two-suited with spades & the bid minor (forcing)
• 2S followed by a jump to 3S over 2H = Two-suited with both minors (forcing)
• 2S forcing 2NT followed by 3NT = Shows a big three-suited hand (forcing)
• 2S forcing 2NT, then 4C or 4D = 2-suited with hearts & the bid minor (game forcing)
• 3C & 3D = 1-suited minor hand (forcing)
• 3S (a jump) after 2H negative = Two-suited with both minors (forcing)

Rebids and responses with huge two and three suited hands:

Huge Two Suited Hands: Bid 2S forcing (relays to) 2NT and besides possibly just being a one-suited spade hand, it could show 2-suited or 3-suited hands – depending on rebids

• Spades & a Minor: Bid 2S and then over the forced 2NT response, bid your minor (forcing)
• Hearts & a Minor: Jump to four of your minor with hearts & the bid minor (Roman jumps)
•  Both Majors: Bid 3H (after 2S/2NT) showing a big major 2-suiter (7-6, 6-6, 6-5, maybe 5-5)

Responses:

• 3S = Longer spades than hearts
• 3NT = Equal length in the majors but less than three-card support
• 4C = At least 3-card heart support with spade shortness
• 4D = At least three-card support for both majors
• 4H = Longer hearts that spades
• 4S = At least three-card spade support with heart shortness

Both Minors: Jump to 3S over the 2H negative response showing a minor 2-suiter

Responses:

• 3NT = Equal length in both minors (may be less than 3-cards in each)
• 4C = Longer clubs than diamonds 
• 4D = Longer diamonds than clubs
• 4H = Shows at least a 3-card club fit and shortness in diamonds
• 4S = Shows at least a 3-card diamond fit and shortness in clubs
• 4NT = Shows at least a 3-card fit in both minors
• (3NT responses could be reversed, showing the minor you don’t have)

Huge Three-Suited Hands: Over a 2H response to a strong 2C, after bidding 2S to force 2NT, bid:

• 3NT = Showing a very big 3-suiter
• 4C = Asks opener to describe his 3-suiter
• 4D = Shows both majors and an unknown minor
• 4H = Shows four hearts and both minors
• 4S = Shows four spades and both minors
• 4D, 4H or 4S = Shows a 6 or 7-card suit with no other 4-card suit

With 5-4-4 and a 5-card major, strive to just open your major suit and pray!  With some strong 2-suited hands, just open one of your suits but with a hand so rich in tricks with a modicum of support you expect to make game, then and only then open 2C. The same strategy applies to strong 3-suiters – unless they are absolutely huge, it’s probably best to just open one of your three suits.