Showing that people can related within a genealogical time frame is about all that you can do with Y-STR testing. Sometimes you get a mutation on a very slow marker (rate <.001) that distinguishes one branch. However, there is a lot of serendipity involved. The 38-67 panel has a number of slow markers chosen with this in mind, but few mutations turn up.
Faster markers often mutate again in another branch (parallel mutation), so you need some paper evidence to use them to split the lines.
The Big Y test is the next step. It tests a lot of very slow markers (SNPs), so that a parallel mutation within a surname is extremely unlikely. We do not know yet how many private mutations will show up, since so few people have taken the test. (Note FTDNA's sale on it ends today, but there will likely be others. The price should also go down as they ramp up the test.)
There is another similar test, but it is more expensive.