Prepare the pork by cutting it into 4 equal chunks. Season the meat on all sides with about 1/8 cup of taco seasoning. Set aside the remaining seasoning to use later.
Turn on the Instant Pot sauté feature and add the olive oil. When the olive oil is fragrant, sear the pork shoulder chunks for about 3 minutes on each side.
Once the meat has browned, turn off the sauté feature, remove the meat from the pot, and set it aside. Add 1/4 cup of water to deglaze the Instant Pot and use a wooden spoon to scrape the brown bits from the bottom. Add the crushed tomatoes and remaining taco seasoning to the pot. Mix well. Place the trivet inside the Instant Pot and place the seared meat on top of the trivet.
Place the lid on the Instant Pot and turn the valve to seal. Turn the Instant Pot to manual > high > and set the timer to 45 minutes. It will take about 10-15 minutes to build enough pressure to start counting down from 45.
Once the timer goes off, quick release the Instant Pot and open the top. Remove the 4 chunks of pork and place them on a large plate or cutting board. Carefully use 2 forks to shred the pork. Discard any fatty pieces and mix the shredded pork back into the Instant Pot.
Add in all of the beans, salsa, and any other add-ins. Mix well.
Serve with Greek yogurt, fresh cilantro, and shredded cheese.