Grammar error correction (GEC) systems have become ubiquitous in a variety of software applications, and have started to approach human-level performance for some datasets. However, very little is known about how to efficiently personalize these systems to the user's characteristics, such as their proficiency level and first language, or to emerging domains of text. We present the first results on adapting a general purpose neural GEC system to both the proficiency level and the first language of a writer, using only a few thousand annotated sentences. Our study is the broadest of its kind, covering five proficiency levels and twelve different languages, and comparing three different adaptation scenarios: adapting to the proficiency level only, to the first language only, or to both aspects simultaneously. We show that tailoring to both scenarios achieves the largest performance improvement (3.6 F0.5) relative to a strong baseline.