The gut can be a breeding ground for a number of infections including parasitic worms, parasitic protozoa, rogue bacteria, fungal/yeast and viruses. As Matt said, testing is very hit or miss, many choose to do a protocol of trial and error.
Klebsiella is a gram negative bacteria. Gram negatives are typically more difficult to get rid of than gram positives, this is due to a double membrane which makes Antibiotic penetration more difficult. Not all natural or pharma drugs work on gram negatives, so keep that in mind.
They (gram negative) can also show signs of resistance. A very good sign of resistance is if you find the right remedy, you should see die off within 7-10 days. If during or after this period, you see a return of the infection, then suspect resistance. Not to worry though, there are many naturals which can bind up the resistance. Let me know if you need a list.