Is it impossible to describe all particles using only 3-branes? Pardon my terminology, I might be using the words wrong. I watched Susskind string theory course, where he explained the attempt to describe particles using vibrating strings instead of point particles. If you do this you need to have more than 3 spatial dimensions or otherwise there is some problem that I cannot remember (I cannot find the part in the video where he talks about this). Then he explained that string theory also predict all kind of other stuff such as d-branes.
My question is: If instead of attempting to describe elementary particles by vibrating open strings, you attempt to do it by vibrating open 3d volumes (so a particle would have a small volume in our 3D space, and an "open" volume, not one closed into hidden higher dimensions), then, would you still need extra dimensions?
 A: 
using vibrating strings instead of point particles.

,,,

you attempt to do it by vibrating open 3d volumes (so a particle would have a small volume in our 3D space, and an "open" volume, not one closed into hidden higher dimensions), then, would you still need extra dimensions?

There is a misunderstanding on how particles are represented in string theories. Analogous to the "point" in the term "point particles" the dimension  is expanded to a string. The point is not represtnting a particular  particle, and similarly  the string is not the particle. All particles in the standard model are point particles, and points cannot be distinguished as to their space characteristics. In the same way, strings cannot be distinguished as to their space characteristics.
It is   the vibrations on the string  which have the group structure that can represent the elementary particle table correctly, with the standard model and its SU(3)xSU(2)xU(1) symmetries. Each particle in the table linked, is assigned/occupies a unique  vibration of the string,
that vibration  has the specific  particle  quantum numbers.
So the " vibrating open 3d volumes" would just make mathematics much more complicated ,   vibrations of the 3 dimensional volume being a lot more  complex.
You would still need extra dimensions.
