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].
This might be obvious, but just to state it explicitly for everyone: you can freeze the weights of the existing layers if you want to train the new layers but want to leave the existing layers untouched.
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