The short answer is yes, but it may be more difficult than you think.
Before Existing Conditions even sends out a project proposal, our consultative sales associates will ask if you need the work to be modeled in a specific template. Our modeling teams routinely work in client templates so that your work can begin immediately upon receiving the existing conditions model. If no such template is specified, we will build the model in our own template.
Once modeling begins, it is very hard to change templates. The best way to avoid this issue is to provide us with your Revit template before modeling begins.
If you have received a model from us, and need to move it to your template, the first step is to try to Link-Bind-Explode. Link our model into yours, bind the link (which will turn the model into a group), then explode the group. Pay special attention to the levels, which will effect not only the views, but the elements within them.
If this does not produce the desired result, there is another (slower) way to move the model to your template. You will simply need to copy everything from our model into your own. While this is indeed a simple process, it is slow and meticulous. Before undergoing this, be sure that both models have the exact same levels (in both name and elevation). We find it helps to copy (or "cut") and paste in pieces. Using worksets can help make this process smoother for large, complicated models.
For example, go to the Level 1 Floor Plan of the old model, and select everything you can see. Copy. Then go to the Level 1 Floor Plan of the new model, and paste. Do this for each level. If the project includes RCPs, those will need to be copied separately. Here are some other things to keep in mind:
Make sure that pinned objects are selectable.
Don't forget to copy the point cloud(s) to the new model. They are very easy to copy/paste, and the links are automatically pathed.
Exterior Elevations (if included) will need annotations, dimensions, masking regions, etc. copied and pasted view by view.
If you do not have the time to do this, or are not confident about the process, don't worry. We will be able to do this for you, though it may impact your project budget.