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I have a 2003 38 Open w/oil change system as well. Assume its the same. System has 5 red valves and a switch (2 position) that allows you to remove or fill the engines, transmissions, and generator. I only use the system to extract engine oil, transmission fluid and generator oil. Normally I run the engines and generator to warm the oil before doing an oil change. After running the engines and generator I start with one engine and do the following:
1) remove the dip stick to allow air to enter the oil pan. (replace following oil change and prior to starting)
2) open the appropriate valve on the oil changer
3) place a 5 gallon pail in the engine room and put the oil changer hose into it and start the systems placing the switch in the "remove" position.
4) once all oil is removed from an engine I shut the switch off and close the valve for that engine on the oil changer system
5) repeat steps 1-4 for second engine and generator. (BTW my boat has a second valve near the generator that goes to the oil changer system that needs to be opened as well)
6) Same procedure is used to remove transmission fluid for each engine..
Once all oil is removed I shut the oil changer off at the breaker panel and ensure all valves on the system are in the "OFF" position.I then refill each engine with 15W40 Rotella T(same for generator). I use Rotella T 30 wt for the transmissions...
Assume you are also changing engine oil filters as well. When changing the filters I preload each filter w/3 qt of Rotella to ensure the engine doesn't starve for oil when starting the first time... M2C

Thanks from me as well.  We have a 2005 38' Open Tiara.  Looks the same as described.