In principle, yes, you can have multiple clauses like this in a shareholder's agreement. When you invoke a clause, you would state which clause you are invoking.
I'm not a huge fan of put/call clauses. I find vesting to be a much cleaner option. Of course vesting implies that you will continue to have your ex-partner holding shares in your company (if they pass the minimal vesting period). In the early stage, a shotgun clause may be reassuring. Over time it loses value and may become an obstacle.
If you are an outside investor in a company which has put/call/shotgun clauses it is a cause for concern. You are backing the people to create the company. With these clauses you never know who you are backing, and if the person you really like is going to somehow leave, have no more interest in the company, and leave everything in the hands of a second person you may not trust as much. Often professional investors will get these clauses taken out of your shareholder agreement before investing. If you want outside, professional money, it is maybe better not to have them at all.