A good coach will take a look at the big-picture when answering your question. The training volume and intensity you performed prior to the first Saturday race may impact the training you do until the second Saturday race - a week later. The distance and difficulty of the first race will also impact training needed or recovery needed after the first race. It is one thing to run a 5k and then a week later run another race, but it's toally different to run a half-marathon and then a week later run a 10k race. Even two 10k races just 1 week apart is taxing and requires recoveries moderate training between the races.
I can't give you an exact answer that fits all situations. Runners I coach know that I will look globally at their unique situation in order to derive a suitable training plan. Self-coached runners need to be as objective as possible and think globally too. Do not let ambition and goals override logic. Mentally step back and consider the circumstances as if you were coaching someone other than yourself. What would you say to a lesser-experienced runner whom you were coaching?
Many years ago, when I raced often, particularly in roac races after college, I would often run 5k races on consecutive weekens and schedule my training as follows:
Sat : am - race; pm - 5 miles EZ
Sun: 5-6 miles very easy
Mon: Long Run at an easy pace (10-12 miles)
Tue: 5-6 miles EZ, with easy striders
Wed: Hardish day - some fartlek, CV reps with 200s, or tempo running with hill charges.
Thu: 6-8 miles very EZ
Fri: 5-6 miles with 8-12 minutes at Tinman Tempo effort, sometimes striders.
Sat: repeat the last Saturday.
If I raced a 5-mile or 10k on the first Saturday I'd do quicker intervals or fartlek on Wednesday since the overall pace of the first Saturday race was slower. If I ran a half-marathon (which happened only twice in my life), I did not race the following week, no matter what, because I know it's not enough time to recover. I raced 2 weeks later in a 5k or 3 weeks later in a 5-mile or 10k race.
The important messaages here are:
- adjust your training to match your race severity and frequency
- a 3-day cycle is not set in stone