Up until now the US, economically, has mostly functioned as a consumer of European and Asian goods, so it is hard to imagine how they could offer an alternative to OBOR. For China it's a way to offload their export driven surplus and creating new markets, which is something that the US isn't really positioned to do.
And most importantly, even those global companies constitute only a fraction of the entire US economy. Most of the US economy is not organised in publicly traded, globalized, businesses.
The bottom line is, as can be seen in the American export and import balance, a strong tendency to consume global goods rather than sell them. The reverse is true for China. That's why China pursues an expansionist economic foreign policy, whereas American economic policy is largely divorced from its foreign politics.