Let me start by asking what questions are you trying to answer? Are you wanting to understand causality or just pick a winner? Can you measure the extraction Y's after each "run"? Are you trying to minimize the number of re-circulations? How are you handling noise (within lot & lot-to-lot variation of the raw materials, ambient conditions, temperature, etc)? Are you planning on replication, blocking or something else?
There are a couple of ways to think about the re-circulation:
1. Create 4 Y's for each of the 4 treatments (2 factors, pressure/concentration at 2 levels). Measure the critical characteristic(s) of the extrusion after each run. Analyze the 4 Y's as multivariate (correlation et. al.). You could also use this data to create a model with the 4 data points and use those to estimate response variables that describe the model (e.g., slope, max, min). Or you could create summary statistics of the 4 data points (e.g., mean, standard deviation)
2. As Mark suggests, a split-plot where the whole plot contains the 2 continuous factors and the subplot contains the 4 re-circulations. This design will take into account to restriction on randomization (which you will need to account for in analysis). Are you planning on any replication?
The most important thing is to capture the data that represents how you acquired it. So let's say you have 4 treatments (4 rows) for the 2 continuous factors (2 columns) . Then 4 columns for each of the 4 circulations (if this is univariate, you will have a table with 6 columns and 4 rows.). Once you have this data, it can be stacked or manipulated to perform analysis multiple ways. It is possible to create this design "by hand".
"All models are wrong, some are useful" G.E.P. Box