**Core Concept**
The question is testing knowledge of the common causes of secondary bacterial peritonitis (SBPE) in the context of a primary E. coli infection. SBPE is a severe and potentially life-threatening complication that occurs when bacteria from the primary site of infection (in this case, the gastrointestinal tract) translocate to the peritoneal cavity.

**Why the Correct Answer is Right**
After an initial E. coli infection, the most common cause of SBPE is a polymicrobial infection involving a combination of aerobic and anaerobic bacteria. However, the most frequently implicated organism after E. coli is Klebsiella pneumoniae. This is because Klebsiella can easily colonize the gut and is known to cause severe infections, particularly in the setting of compromised host defenses.

**Why Each Wrong Option is Incorrect**
**Option A:** This is incorrect because while Enterococcus faecalis is a common cause of SBPE, it is not the most common organism to follow an E. coli infection.
**Option B:** This is incorrect because Staphylococcus aureus is more commonly associated with skin and soft tissue infections, rather than SBPE following an E. coli infection.
**Option C:** This is incorrect because Pseudomonas aeruginosa is a common cause of hospital-acquired infections, but it is not typically associated with SBPE following an E. coli infection.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that SBPE is a medical emergency requiring prompt recognition and treatment. The most common organisms responsible for SBPE can vary depending on the primary site of infection and the underlying host factors, such as immunocompromise or recent abdominal surgery.

**Correct Answer:** D. Klebsiella pneumoniae