US President, Joe Biden, recently suggested that the US Government would be in favour of a waiver of patent protection surrounding COVID vaccine development. Whilst the US is only one country at the WTO and they generally only act on consensus, it will certainly make other countries think hard.
To be honest, though, I can't say I'm in favour of a patent waiver here. Avoiding the patents of other pharmaceutical companies isn't the "hard problem" in the pandemic environment we find ourselves in; getting hold of the ingredients to manufacture at global scale is.
All of the different manufacturers are reporting difficulties obtaining ingredients and other supplies. They are reporting challenges with export/import across the world between suppliers and their many manufacturing companies.
So, the most effective way to increase supply of the COVID vaccine is to get all the paperwork out of the way – make a global single market for COVID vaccine related supplies. Make sure that every single country that can manufacture supplies for the various vaccines available is able to supply them with the least amount of fuss. It should be easy for, say, a supplier in Ghana to supply the Serum Institute (the world's largest vaccine manufacturer, btw) in India – not hard.
Of course, if there is less paperwork, there will also be lass overhead on the eventual cost of the finished product – and that should be reflected in the price charged to countries that can least afford it. By law, if necessary.