I participated in a secondary offering and sold shares. They charged transaction fees and other fees. Do I add these to my cost basis?

Your cost basis is usually your total cost of the asset, including transaction and other fees.
See https://www.irs.gov/taxtopics/tc703

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You are correct.  It will be included in the cost basis:

TurboTax has made allowances to make this correction. 

1. When posing in the Stock area there is a check box.
2. Under Box 1e - Cost or other basis 
   1. Report the basis as it shows on the brokerage firm
3. Below that you will see 
   1. The cost basis is incorrect or missing on my 1099‑B
   2. Check this box and .. Continue
4. Let us know if any of these situations apply to this sale
   1. ​​​​​​​None of these apply .. Continue​​​​​​​
5. We noticed there's an issue with your cost basis...Let us know if you'd like to make any changes
   1. I know my cost basis and need to make an adjustment
   2. Enter the adjusted amount