Stuttering is a varied speech disorder that harms an individual's communication ability. Persons who stutter (PWS) often use speech therapy to cope with their condition. Improving speech recognition systems for people with such non-typical speech or tracking the effectiveness of speech therapy would require systems that can detect dysfluencies while at the same time being able to detect speech techniques acquired in therapy. This paper shows that fine-tuning wav2vec 2.0 [1] for the classification of stuttering on a sizeable English corpus containing stuttered speech, in conjunction with multi-task learning, boosts the effectiveness of the general-purpose wav2vec 2.0 features for detecting stuttering in speech; both within and across languages. We evaluate our method on FluencyBank , [2] and the German therapy-centric Kassel State of Fluency (KSoF) [3] dataset by training Support Vector Machine classifiers using features extracted from the finetuned models for six different stuttering-related event types: blocks, prolongations, sound repetitions, word repetitions, interjections, and - specific to therapy - speech modifications. Using embeddings from the fine-tuned models leads to relative classification performance gains up to 27% w.r.t. F1-score.