Now on to continuous filtering. I found virtually no information on this other than a mention of it being a type of filtering. With continuous filtering you're going to add the DE to the syrup while you're filtering.
To do this you're going to need to know how many gallons your draw off container will hold and set a target level to add the DE. For example when you reach your target level add the amount of DE for that quantity of syrup and begin filtering. Keep an eye on the syrup you're filtering and add more DE when you reach the target level again or when you can't see much DE in the syrup to being filtered. You can guesstimate here as to the number of gallons that has come into your draw off container since you started the press and add the appropriate amount of DE.
In some cases you're going to empty your draw off container waiting for syrup to come. In that situation shut off the press and wait until you reach the target level again, add DE and restart the press.
It's okay to shut off the press for short periods of time and start again without doing anything to keep the press hot. If that period is going to be long enough for the syrup coming out of the press to be below 180* pump the syrup back into the draw off container until it's hot enough to continue filling containers. The pressure will be a little higher when you start out but will come back down as the press comes up to temperature.
Someone on this forum said that he let his press sit until the next day and was able to start it again and filter on. I tried it myself to see if it was possible or if it was bs. It was very sluggish and the pressure was real high at first but it did work and I was able to get another day's boil through it without changing papers. As a disclaimer here, I don't recommend that you run your press this way! I only did it to see if it was possible.