Are there more than four dimensions?
We only know for certain that there are four dimensions.
General Relativity (GR) describes the universe in terms on for dimensional spacetime. We have three spatial dimensions and a time dimension.
The problem is that GR and Quantum Theory are both proven in many respects but are incompatible.
Clearly we need new physics which can unify GR with quantum theory. One set of candidates for this is string theory. This requires adding six or seven extra dimensions. There is no evidence that string theory is correct. In any case the extra dimensions would have to be very small. Think of a particle being a vibration along the axis of a very small dimension. The extra dimensions have no meaning in terms of space and time.