One partner is refusing to sign a amendment shareholder's agreement, which would bring in a large investor

We started our small corporation 2 years ago with 3 partners - lets, call them Adam, Ben and Carl for argument's sake. Adam and Ben do all the work. Carl turns out to be a louse who is always angry and complaining about something and does no work. Adam and Ben successfully grow the business and try to ignore Carl while remaining as cordial as possible. Adam and Ben get a first round investor interested who is willing to put in a large amount of money for 10% of the company. Lawyers on both sides spent months to work out all the details and everyone is happy, until Carl becomes angry at Adam and Ben over a perceived hurt - which is not based on any facts. Now Carl is refusing to sign the amended buy-sell shareholder's agreement. This would have a significant negative impact on the future of the company. Can Adam, Ben and the new shareholder sign the agreement without Carl? What can be done if Carl refuses to sell his shares but continues to not want to sign the amended agreement?

It depends entirely on what legal agreements you have in place with Carl, so you would have to consult a lawyer who would read your particular legal agreements and advise you on what they say.

If you started the company the right way, using an experienced venture lawyer, when you looked closely at those agreements, you would probably find that you have the right to fire Carl, and take back his unvested shares. If the agreement was typical, that would be about half of Carl's shares. You might also find that either:

1. you had the right to force him to go along with the investment, or
2. he had the right to veto the investment.

Either option is common. It entirely depends on what is written in the agreement. You'll have to read it.

You might also find that:

1. you have the right to purchase his shares under certain circumstances, and/or
2. you have the right to make an offer to purchase his shares, and if he refuses, he is obliged to purchase your shares.

Either option is common. It depends entirely on what is written in the agreement.

So, there's a theme here: It depends! I am not a lawyer and this does not constitute legal advice.