Went through offer negotiation with Two Sigma for a senior SWE role in NYC last fall. Sharing what worked and what didn't, because most negotiation advice is too generic to be useful for a place like this.
What I came in with: a written competing offer from a large tech company (you know the names). Base was within $10k of what TS offered but the stock was worth significantly more in current market value.
What I asked for: higher base, higher signing, and asked if there was flexibility in the bonus target.
What moved: Signing bonus went up by $15k after I pushed once and referenced the competing offer. The recruiter went back to the team and came back within 2 days.
What didn't move: Base was firm. The recruiter said the base band for the role was set and didn't have room. I believe her; the band felt real, not just a negotiating position.
Bonus target: they would not move the target percentage. What they said, and I found this interesting, is that the target is less meaningful than the actual payout history. They hinted that the payout has often been above target for this team. Hard to verify.
Overall impression: Two Sigma negotiates differently than big tech. They have fewer levers to pull. The signing is the flex point. If you have a real competing offer, use it immediately in the first negotiation call. Don't do the thing where you reveal it slowly. They respond to clear data.
The recruiter was professional throughout and the process didn't feel adversarial. My sense is they value candidates who negotiate clearly without drama, which honestly is how I prefer it anyway.