The better alternatives can include Raytheon upgrading their tech. But more likely it will be something other than Raytheon missiles.
The US (and presumably Taiwan and other allies) is also learning from Ukraine. This is a two-way street. Ukraine has already produced many innovations in the use of SAM systems, in defensive use vs cruise missiles, plus “offensive” operations vs fighter bombers.
Tech upgrades are always ongoing, but we are unlikely to hear anything about them within the time frame that they are relevant.
Also, Patriot will not be the primary US weapon system at the beginning of a China war. Those would be Navy shipboard systems. US bases with Patriot deployed will not face the worst of Chinese capabilities, they are too far away from most Chinese missile types.
Taiwan will depend on Patriot for some of its air defense needs (they have a bunch of other relevant, shorter range systems), but the odds are that these will be swamped by initial waves of Chinese cruise and ballistic missile attacks. I figure they have 42x4 cell launchers in 7 batteries, plus a reload. It will take too long to reload, the missiles in any given wave will get through. China can generate much larger numbers of missiles than Russia could or can. Whatever is going to Ukraine will be a drop in the bucket.
I am assuming that a Chinese operation vs Taiwan will be a medium term thing, unless current tensions escape beyond the control of the Chinese high command.