In general this is of course an active area of research, but yes, you can do something that and people have done it successfully[1] by adding extra layers to an existing model and then continuing to train it.

You have to be careful about the "same data" part though; ideally you want to train once on unique data[2] as excessive duplication can harm the performance of the model[3], although if you have limited data a couple of training epochs might be safe and actually improve the performance of the model[4].

[1] -- https://arxiv.org/abs/2312.15166

[2] -- https://arxiv.org/abs/1906.06669

[3] -- https://arxiv.org/abs/2205.10487

[4] -- https://galactica.org/static/paper.pdf