Is it OK to analyze all measures as independent data in paired dataset

I have data from triple-crossover study. Same patients received a drug in the morning then in the noon then in the evening and different parameters were measured. I have 60 lines of data (60 patients) that I compare using tests for paired data to see do this parameters differ between three time points. However, I would also like to analyze correlations between measurements.

Question is, is it legitimate to analyze all 180 (3x 60) measurements and see correlations with other parameters to gain more power? Individual patients will be represented for 3 times this way.
If not, I have only 60 measurements per time point that I can correlate with other parameters and provide analyses for specific time point only.

Someone help please