My recent campaign has been run in arcs of 4 to 6 month, between which we usually change system and rebuild the characters due to using a Work-In-Progress custom system. My players and I have been curious about using D&D a few times, but the leveling curve is bugging me.

My problem is that I do not expect the players to gain more than 3 levels during the course of an arc. Most classes gain a single major feature per level that may not be interesting for the player. Most numerical features increase every 2 or 4 levels. Same for spell-casters unlocking a new spell level. This is especially a problem because in our current system, level-ups give a lot of options and possibly very useful features, closer to the effect of a new archetype or a feat.

For this reason, I would like to let players take 2 character levels instead of 1 during a level-up, so as to make sure that their features upgrade and that they get at least a new one that interests them. If they like all of it, all the better. Over the course of an arc, instead of going from level 3 to level 6 (gaining a feat, a damage upgrade at 5 and a usually non-combat feature before the finale), they would go from level 3 to level 9, unlocking the usually much more impactful features of level 9 and/or 10.

Are there any unintended negative consequences to this?

For the record, we use Milestone leveling for simplicity. The players can expect at most three major level-ups during this time, those usually gave to completely new abilities or huge power spikes. The gameplay itself is usually light in combat, although a D&D game would probably have more.

You know your players

As long as you are scaling the encounters to match their ramp up of levels, this sounds like a fun way to get players to feel like heroes faster. If this is going to have them enjoy the game more, go for it.

The only downside I can think of is gaining a feature AND an ability score increase is a large power jump, but if the encounters are equally hard, it's fine. Taking fighters for example, they get their first ASI at level 4 and a landmark feature of having an Extra Attack at level 5. So going from Level 1, to 3, to 5, could be a really big jump for the party so its worth being extra cognizant of that.

Another issue could be that they may not become intimately aware of all their skills or interactions that could take time to develop a feel for, but if they are experienced at TTRPG's I don't think that's an issue at all.

You have to be wary of the spikes in character Complexity

I'm going to use the Rogue as an example because this class represents the most obvious manifestations of how this kind of rapid leveling could be an issue; but in general, this is an issue that affects most classes and most levels of play.

Consider the first level. A level 1 rogue has the following features they need to contend with:

• 
  Sneak Attack—Extra damage when they have advantage or able to benefit from Flanking


• 
  Expertise—An especially high bonus to certain skills, meaning they will excel at certain kinds of ability checks


• 
  Thieves' Cant—A "secret language" that can have interesting RP consequences.

Those are quite a few features, but it's balanced out by the fact that they'll be spending some time at level 1, only dealing with those features. They'll have time to work out how each feature works and how to best make use of them.

When they hit level 2, they're only gaining one additional ability, but it's a pretty significant ability:

• 
  Cunning Action—simply gaining a few uses for a character's Bonus Action can completely change their combat style all at once. Being able to Disengage as a Bonus Action completely changes a character's relationship to the layout of the combat encounter, with respect to creature positions, geography, etc.. It's a lot.

Then, at Level 3, comes the archetype features. Every single archetype gains at least 2 new features. Even for archetypes like the Thief, where one of their features just improves upon the Cunning Action feature, the other feature is also giving some movement bonuses (or removing movement penalties).

If they're an Arcane Trickster, then they're getting

• 
  Mage Hand Legerdemain—an extension to their Bonus Action abilities


• 
  Spellcasting—and this is everything
  
  
  • 3 new cantrips, one of which is Mage Hand
    
  
  
  • 2 Spell Slots
  
  
  • 3 new Spells (2 Illusion/Enchantment, 1 any school)
  
  

Now let's see what this feature gain looks like if we include level 2:

• 
  Cunning Action—simply gaining a few uses for a character's Bonus Action can completely change their combat style all at once. Being able to Disengage as a Bonus Action completely changes a character's relationship to the layout of the combat encounter, with respect to creature positions, geography, etc.. It's a lot.


• 
  Mage Hand Legerdomain—an extension to your Bonus Action abilities


• 
  Spellcasting—and this is everything
  
  
  • 3 new cantrips, one of which is Mage Hand
    
  
  
  • 2 Spell Slots
  
  
  • 3 new Spells (2 Illusion/Enchantment, 1 any school)
  
  

Do you see the problem? There's a lot that a character is gaining in terms of features just going from levels 1 to 3. As a consequence, it's quite easy for one or more of those features to fall through the cracks and forgotten.

Now let's just take this same character and jump them to level 9, without doing the step-by-step, and just see how many new features are showing up:

• 3 new spells (2 Illusion/Enchantment, 1 Any School)
  
  
  • and the ability to replace up to all 6 of their spells with something else entirely, adhering to those school restrictions
  
  


• 2 Ability Score increases or Feats (are the feats adding new features?)


• 
  Uncanny Dodge—this dramatically changes their relationship to especially strong melee creatures


• 
  Evasion—this changes their relationship to powerful spellcasters


• More Expertise—more skills they can use to trivialize certain kinds of ability checks


• 
  Magical Ambush—creates a very powerful use for their Cunning Action/Bonus Action Hide ability

This is a lot to keep track of! Each of these features have significant impacts on how this character would play on a moment-to-moment basis, and if these are things that the player can't keep track of, it'll dramatically reduce their power level.

This is less of an issue in normal play because you normally advance through these levels over the course of months or even over a year or two. There's a lot of time to work out how each feature improves upon the character they're playing. But compressed into the weekend or two between sessions, it could be too much.

Experienced Players can probably handle these changes—Probably

It should go without saying that if you trust that your players are either experienced enough or smart enough to be able to take these kinds of complexity gains in stride without struggling to keep track of their new features, then you have a lot less to worry about. I know there are lots of players—especially people who are used to playing Rogues—who would scoff at the list I've posted above and say "what, that's all I need to deal with?"

So I'm not here to tell you this is a bad idea, or that your campaign is going to suffer if you choose to do this. All I'm going to tell you is that if you plan to do this, it is very important that your players understand what you're signing them up for, and are prepared to deal with it. If they are, then I imagine this is a good way to quickly get players to a Tier of play that tends to be somewhat underrepresented in 5th edition.

Just be mindful that even experienced players might be playing a class they haven't touched before, and that they could get overwhelmed by having too many new features to keep track of.

In my experience, handing someone a high-level D&D character in any modern edition (since 3e at least) is a recipe for frustration.

Expecting someone who hasn't played a lot to create a high-level D&D character is also a recipe for frustration.

As you play D&D you, the player, gain expertise both with your specific character, and with the mechanics of D&D. The level based design of D&D is intended to have complexity of your character increase as you get better at both D&D and playing that specific character.

In 5e specifically, at each level a character 0 to 2 features. How these change how the character plays is meant to be learned over the course of a level (or two), at which point the character gains a new feature and the player has new things to learn.

By doubling up level increases you to steepen this learning curve a bit.

That is about the only downside.

Now, 5e D&D's power curve is a bit more linear than 3e/4e's power curve. So if you want each of the increases to feel equally large, may I suggest:

3/5/8/12

For a 12 con d8 HD character your HP will follow:

21/33/51/75

So 57%/55%/47% increase in HP in each of those bumps.

You get 1 "baseline" ASI per milestone this way, and have access to the level 11 at-will attack boost for most characters.

Another really important difference is that you unlock the level 11 at-will attack boosts; Fighter 3rd attack, Paladin auto-smite, various Cantrip upgrades, etc.

Hard To Keep Gear Levels Right

Other answers have hit the big issues, but have you considered what this does to selection of magic equipment? If you're halving the time it takes to get to a certain level, you need to double the rate of non-disposable magic items being obtained just to be where they "should" be at that level. If you don't increase this equipment gain, you will find the characters even more reliant on their natural abilities which, due to their rapid level gain, they may not have the out-of-game knowledge to use effectively.