Sure you can, let's see...
I've searched for "penny stocks trading" (just for example, as I think it is pretty competitive keyword). I did my search in .com, co.uk and com.sg (of the same famous SE).
And I found out that 6 out of 10 results (all are .com) came up in all 3 searches.
I think that this shows that it is possible to rank well in more that one countries.
What do you think?