Would K-means be Appropriate to Use with Four or More Variables?
You can use k-Means clustering in all the dimensions you need. This technique is based on a k number of centroids that self-adjust to the data and "cluster" them. The k centroids can be defined in any number of dimensions.

If you want to find the optimal number of centroids, the elbow method is still the best. You iterate the algorithm changing the value of k each time, and record how much error the clustering is producing; once you're done you plot the error levels against each k value and check the optimal k visually. There is plenty of tutorial on it, you can start here for example.