For a "traditional" game:
Multiple types of shots, options and spell cards per character, as item collectables. These would float around the screen and change type based on time. Ideally, these different types would give scoring routes some depth. I think the ideal number is 3 of each shot, option and bomb type for each character.
More bomb items. I want a game that encourages creative usage of bombs, and having multiple bomb types complementing a strong system, while you mind when you pick up what type of bomb in order to plan your bomb types for various situations, would be favorable. In order for this bomb system to work, you could have 3 bomb "slots", which can be filled up with a bomb item. Bomb slots cannot be used unless filled up, they start out empty and dying does not fill them up; you have to collect items.
Grazing to up the spellcard value and player controlled opportunity-based grazing in general could definitely be brought back by now under a new guise. The former is more important to me than the latter.
Ground enemies wouldn't be too shabby, i.e, enemies you can't collide with and with deadzones.
Longer and more involved stages would be necessary for some of these ideas to be any good.
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For a Phantasmagoria:
Grazing to affect number of bullets sent over to the opponent, more types of bullets/patterns that are suitable for grazing, no pellet bullets but have different types of ex bullets, no bullet reflection, enemy chaining summons bosses as usual, boss behaviour is not random but pattern types are used in succession and depends on how big the chain is, you always have 3 lives and lose 1 when hit, you have 2 bombs which is not part of your spell gauge but does affect the opponents screen, consistent ai timers