You can use ReplaceList for something like this... Cases is hard. I tried all sort of ways for that, but as Daniel says, it requires more creativity than I certainly have.
In[1]:= test = {{1, {2}, 3}, {2, 3, 4, 3}, {3, {3}, 4, 3}, {4, 5}, {6, 7}, {4, 5}}
Out[1]= {{1, {2}, 3}, {2, 3, 4, 3}, {3, {3}, 4, 3}, {4, 5}, {6, 7}, {4, 5}}
In[2]:= ReplaceList[test, {___, y : {__, 3}, z : {__, 3}, ___} :> {y, z}]
Out[2]= {{{1, {2}, 3}, {2, 3, 4, 3}}, {{2, 3, 4, 3}, {3, {3}, 4, 3}}}
