How to find similar points to a positive set when you don't have any negative set?
To summarize, you have labeled data in one class (positive) and unlabeled data. You want to find the positive examples in the unlabeled data. The general name for this setting in machine learing is one-class classification, which is a fairly broad field.

A sub-area that is particularly relevant is positive-unlabeled learning, which is the problem of training a classifier when one has just positive and unlabeled data.

Also note that you have all the examples that need to be predicted at training time. Therefore you can use a transductive learning algorithm. Particularly, if you have a notion of which companies are similar, you could construct a graph by connecting similar companies by edges. You could then run a graph propagation algorithm that would assign scores to the unlabeled items.

Finally, here is a similar question where the answer suggests a method of positive-unlabeled learning.