MLR equivalent for repeated measures, multiple correlated responses

I'd like to determine the best approach to determining effect sizes for a set of experimental data with multiple correlated responses. Due to repeated measurements and high correlation between responses, I know that a simple multiple linear regression model obviously isn't the answer.

The situation: atmospheric gas measurements were taken from specific locations around various vessels over a number of days. Different vessels were sampled on different days, not all units have repeated measurements, and not all locations were always sampled at each unit. The variables are:
  • Sampling date (4 different days spaced weeks apart)
  • Number of days since last maintenance
  • The specific vessel (8 vessels)
  • Vessel pressure
  • Gas level at each sampling location (6 locations)

The key objective is to determine how pressure affects gas level, overall and at each location. Because of diffusion, etc., the gas levels at each location will be highly correlated with each other.

Under a multivariate framework (PCA, PLS), it makes sense to set each gas level location as its own variable, because the latent variable model will take into account the correlation between sampling locations. Unfortunately my dataset is very small, and the large number of categorical variables makes PCA/PLS intractable. Would it make sense under a different model to rearrange the data with two variables: a categorical "sample location" and a continuous "gas level"?

Any help is much appreciated!