Hi Esther,
When I was running my firm in Portland a few years back we got transit cards for each person of the firm that were set to autofill using our company credit card (thus the expense was automatically linked to our Quickbooks Online). Of course this becomes more complicated now that a lot of public transit systems are scanning phones with apple/google pay, so you will have to check if there is a way in NYC for the scan to use the company card vs a personal payment account.
You can also look into Navan: https://navan.com/
They help with company travel expenses and I believe can do flexible spending accounts as well.
Feel free to reach out directly if you have further questions: lucas@charrettevg.com
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Lucas Gray, Assoc. AIA, SEED
Charrette Venture Group
Brooklyn, NY
https://lucasgray.substack.com/------------------------------