TuneTables is a novel prompt-tuning technique for prior-data fitted networks (PFNs) that significantly improves their performance on large datasets. PFNs, like large language models, use pretraining and in-context learning to achieve strong performance on new tasks. However, they have limitations, such as being unable to handle datasets larger than 1000 samples. TuneTables addresses these limitations by compressing large datasets into a smaller learned context, enabling PFNs to scale effectively. It achieves competitive performance with state-of-the-art tabular classification methods, such as CatBoost, on datasets up to 50,000 samples, and even outperforms them on larger datasets. TuneTables also allows for multi-objective optimization, such as balancing accuracy and fairness, and can be used as an interpretability tool. Additionally, it mitigates biases by optimizing fairness objectives. The method is efficient in inference time compared to TabPFN, despite requiring more training time. TuneTables is open-sourced and has been tested on various datasets, demonstrating its effectiveness in improving performance and scalability. The results show that TuneTables significantly outperforms existing methods in accuracy and fairness, while being more efficient in inference. It also enables the handling of larger datasets and more classes than traditional PFNs. The method is flexible and can be applied to a wide range of tabular data tasks.TuneTables is a novel prompt-tuning technique for prior-data fitted networks (PFNs) that significantly improves their performance on large datasets. PFNs, like large language models, use pretraining and in-context learning to achieve strong performance on new tasks. However, they have limitations, such as being unable to handle datasets larger than 1000 samples. TuneTables addresses these limitations by compressing large datasets into a smaller learned context, enabling PFNs to scale effectively. It achieves competitive performance with state-of-the-art tabular classification methods, such as CatBoost, on datasets up to 50,000 samples, and even outperforms them on larger datasets. TuneTables also allows for multi-objective optimization, such as balancing accuracy and fairness, and can be used as an interpretability tool. Additionally, it mitigates biases by optimizing fairness objectives. The method is efficient in inference time compared to TabPFN, despite requiring more training time. TuneTables is open-sourced and has been tested on various datasets, demonstrating its effectiveness in improving performance and scalability. The results show that TuneTables significantly outperforms existing methods in accuracy and fairness, while being more efficient in inference. It also enables the handling of larger datasets and more classes than traditional PFNs. The method is flexible and can be applied to a wide range of tabular data tasks.