Yes, you can apply more than one login along with skip logic, but specific ones only. Such as Show/Hide Questions, Show/Hide Options, Dynamic Text/Comments, Scoring without branching on the score, Quota control, Extraction, JavaScript logic, and update variables these logics are possible to apply.
Along with skip logic, you cannot use compound branching logic and scoring logic with the branching on-score feature, rest all of the logic types can be used.