How to navigate through an offer conversation to get a higher TC?

I am a university student who will graduate this year, and on this Tuesday (tomorrow) I will be having an offer conversation with the startup that I interned at this summer. I have watched the negotiation course and it certainly has provided invaluable information, but there are just some details I want to get opinions from the community so I can maximize my compensation.

First, some facts:

• From what I gathered from the Internet and people working there, the base and bonus part of the package will be slightly lower than FAANG, despite the company considering itself to have a higher hiring bar. I don't see this company going public any time soon, so I will consider the equity as paper money.
• I'm in the process with two other top-tier companies (TC > 220k even w/o negotiation) but both are still in the early stages. I should be able to finish both interviews before the offer deadline.
• My feedback from the internship has been extremely positive (basically my feedback was "keep doing what you are doing").

Based on what I've learned from the course, I think my strategy for negotiation is as follows:

• Disclose as little info as possible on the call as possible. Do not express that I want a boost in TC on the call. Try to defer everything to email with something like "I need to collect all the data I have before making this huge decision". But at the mean time I should at least ask some questions about the offer to show my interest.
• In terms of the components in the package, I should prioritize base, bonus, and sign-on instead of equity.

And after the call, I'll have two options:

• Ask for an increase in TC before finishing the interview with the two other companies, because if I get rejected and I will lose the leverage.
• Do this after the interviews finish. This presents a higher risk, but also a higher reward.

So my main question is which option is better, because I don't know how much stronger an actual competing offer is than an ongoing interview, and I cannot tell how likely I'll pass the other interviews yet.

Two other questions

• Should I explicitly say how much more I want? If so, what is the right amount to request? Match FAANG in cash? Exceed FAANG in cash because equity is too uncertain and according to the company itself, the hiring bar is higher?
• Should I split my request into multiple small increments or just tell them "give me this amount"?