Building a crime syndicate with Blades in the Dark?

It depends which bits of the Blades system you want to use. Are you thinking about:

• The "Faction game" of tracking factions, claims, and standings?
  
• The job/downtime rhythm?
• The system of Actions with position/effect and consequences?
• The notion of flashbacks to avoid the planning bog?
• The use of Stress to avoid consequences, this giving the feel of clever, competent scoundrels?

Because I think you can blend any or all of these into the Blue Planet setting and existing Synergy system, depending on what you want the resulting game to be like.

Blades has many parts that come together to give the whole experience. My question was about which parts of that experience you're after.

The Faction Game, job/downtime rhythm, and flashbacks should port easily to Synergy. You may want to have the more demanding flashbacks the Synergy Strain currency to keep them limited. You can use a Synergy Track to measure BitD Heat, representing how much attention the crew is getting from law enforcement and the world in general.

At a basic level, the BitD Action systems do much the same job as the Synergy Skill Sets.

The interaction of Consequences and Stress in BitD needs more attention if you want to bring it across. With Blades, most actions you attempt lead to some sort of consequence, and the player can spend some of the PC's Stress to avoid those consequences. In play, that leads to a feeling of competent characters dealing with the unexpected and moving past it, and it allows the GM to show how dangerous situations are without artificially pulling their punches.

It's not obvious to me how you'd get that same feeling in the Synergy system without importing a lot of that system, and that would mean a lot of changes to how Synergy works.

Does that help? As I said, it's difficult to answer the question of "importing bits of BitD to play a crime syndicate" without knowing what parts of "play a crime syndicate" you want to import from Blades.

Ah, I think I understand now. Sorry for not getting the point.

Yes, I think the Faction Game side of things should work well with Synergy, in an environment where there are lots of factions to pay attention to! I imagine it would be less useful in a small town, or where the PCs are say Sunburst poachers who only come to town briefly to sell the hides.

The Downtime/Job split is also easy to bring into Synergy, so long as there are enough distinct things to do in Downtime (BitD has actions like "Remove Stress", "Heal", "Pursue long-term project", etc.) that warrant breaking it out into a separate, formal stage of play.

The other game worth looking at is A|State, a fairly recent game (at least, this edition) based on the same rule set. It broadens the scope of the game a bit, from criminals and scoundrels to a game of people in a city making their own corner a bit better. It's a game about hope and building community in a world that doesn't care. I can easily see that driving a game of the urban underclass in one of the big Poseidon settlements like Haven, Second Try, or Harmony.