I'm facing a similar challenge. Although I'm totally NOT an expert on this function, Linear Mixed Models allow you to flexibly design a model, with multiple factors (which can be nested). In your case, it seems to me that you need to add another (within) factor, which is the replication/measurement occasions or whatever you want to call it.
I'm not sure but based on what you say, you're using 'GLM Repeat Measures' in SPSS, which is less flexible. However, it might still be possible with that function by adding another factor, like I mentioned.
Hope that is of any help, good luck!