How do I continue to train the model but for different tasks？

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### Bug description

I have obtained a model named last.ckpt by using lightning training. I want to continue training this model. The structure of the model remains unchanged, but the training task has changed, so the hyperparameters have also changed. But when I tried to use resume_from_checkpoint in Trainer, it reported an error and asked me that the hyperparameters for both training tasks needed to be the same.
I want to know how I can apply the trained model to training for other tasks.

### What version are you seeing the problem on?

v1.6

### How to reproduce the bug

_No response_

### Error messages and logs

_No response_

### Environment

Current environment

```
#- Lightning Component (e.g. Trainer, LightningModule, LightningApp, LightningWork, LightningFlow):
#- PyTorch Lightning Version (e.g., 1.5.0):
#- Lightning App Version (e.g., 0.5.2):
#- PyTorch Version (e.g., 2.0):
#- Python version (e.g., 3.9):
#- OS (e.g., Linux):
#- CUDA/cuDNN version:
#- GPU models and configuration:
#- How you installed Lightning(`conda`, `pip`, source):
#- Running environment of LightningApp (e.g. local, cloud):
```

### More info

_No response_

cc @justusschock @awaelchli

Start by reviewing the v1.6 Trainer documentation for resume_from_checkpoint and the checkpoint-loading API, using last.ckpt as the example. Determine whether the intended workflow is resuming training or loading model weights for a new task, and verify how changed hyperparameters are handled. Done means confirming or documenting the supported procedure.

Written by the indexing model from the issue text.