The US used to be able to fight multiple parallel wars, but has demonstrated it can fight at best 1.5 wars — delay/hold on one while fighting the other. It’s possible that in an all out situation, the US could focus more on winning vs. casualties (civilian or own-forces), and maybe fight 1-2 simultaneous conflicts while holding down a few others, but that would be a stretch politically and logistically.
Almost no other countries maintain force projection capabilities (strategic airlift like C-17s and tankers, global sealift and sea control), so it’s highly likely the US would be the only combatant in each sphere of operation, augmented by regional or local allies (e.g. Australia for SEA conflicts; Japan in East Asia; France in North Africa). The UK, maybe Canada would make some effort to contribute in some randomly selected conflicts, but fundamentally the US would be doing the majority.