Just over a month into being a Plat charge cardholder, I thought I'd update this thread with the tale of my try-to-get-a-big-soft-limit-quickly journey in case anyone else is searching for the same info in the future.
Short version: you can increase your soft limit
very fast if you put your mind to it, are willing to make prepayments, and can put big $$ through the card.
Longer version / timeline:
1) Signed up for Plat charge and was approved around 16th of March.
2) Initial soft limit was only $9,000.
3) Put approx $140k through the card in the first month. For the first couple of weeks / $95k or so of charges my soft limit slowly increased - I was having to prepay 70-90% of the charges over-and-above the initial $9k soft limit, with the proportion of pre-payment required slowly decreasing each time I put a big charge through. IIRC, by the time I'd put c.$95k through the card I'd had to pre-pay about $65k of that.
Sometime towards the end of the month my soft limit shot up quickly, with the last $45k going through with no prepayment required - so at the end of the statement cycle I'd prepaid just over 50% of the totle charges that went through the card during the billing cycle.
4) Received a call from someone in Amex's credit team a few days after the end of the statement cycle wanting to discuss my usage of the card. He told me the main purpose of the conversation was to help establish my soft limit going forward, based on how I was / would be using the card. Wasn't too probing, just wanted to know whether the first month represented the norm going forward, whether the charges from the first month were business or personal (mostly business), querying the regularity / nature of charges from the couple of merchants which represented the biggest proportion of the spend, etc.
Once he established that most of the charges were business-related he did ask if I could send a copy of the businesses' financials to them so that their commercial credit team could look at "commercially underwriting" the card, but I declined. He was fine with that - asked me a couple of additional questions about the business (years established, revenue last FY, etc) which I was happy to answer, and left it at that.
5) I spoke to their credit team yesterday to find out what the soft limit would be once I'd paid the outstanding balance in full. Was told $187k, which, based on info posted earlier in this thread, appears to be the maximum they'll support without seeing tax returns / financials and performing a capacity assessment.
Overall I'm very happy with the outcome: I wanted to get the soft limit as high as possible as quickly as possible but was expecting it would take a few months of significant prepayments to reach a high soft limit, not one month
To end on a funny note: when reading the above, bear in mind that this is the same company who rejected my application for the complementary Plat Reserve CC two weeks ago, and after being pushed approved it with a limit of $3,000. $187k OK on one card, only $3k OK on another, same customer...