Assuming I simply want additional credit to improve my credit utilization ratio, how frequently (how long between requests) should I request the credit increases? What negative consequences should I be concerned about if I request credit too frequently, and how big of a problem might that reasonably be?
I don't know of a guideline to how often you can ask for an increase. You can ask as often as you like.
As for consequences, refer to Is there a downside to asking for a credit increase?, where the consensus is that, aside from a possible (temporary) hard pull on your credit report, there's probably no risk to asking.
Depending on your credit score/history, and especially in the current economy, you may get "no" as an answer most often. You can try talking to your card's Credit Department or even Customer Retention Department as they may have more leverage. They may say yes or no or that they need to review your account.
When you do ask for an increase, I would make sure to ask if there will be a hard pull on your report, if there is any cost or downside to applying, and to make sure that this would be an increase to your current credit line, not a new account.
I do this all the time, my credit rating over time plotted on a graph looks like saw blades going upward on a slope
I use a credit alert service to get my credit reports quarterly, and I know when the credit agencies update their files (every three months), so I never have a high balance at those particular times
Basically, I use the negative hard pulls to propel my credit score upwards with a the consequentially lowered credit utilization ratio, and the credit history.
So here is how it works for me, but I am not an impulse buyer and I wouldn't recommend it for most people as I have seen spending habits:
Month 1: charge cards, pay minimum balance (raises score multiple points)
Month 2: PAY OFF ALL CREDIT CARDS, massive deleveraging using actual money I already have (raises score multiple points)
Month 3: get credit report showing low balance, charge cards, pay minimum balance ask for extensions of credit, AND followup on new credit line offers (lowers score several points per credit inquiry)
Month 4: charge cards, pay minimum balance, discretionally approving hard pulls -
always have room for one or two random hard pulls, such as for a new cell phone contract, or renting a car, or employment, etc
Month 5: PAY OFF CREDIT CARDS using actual money you have. (the trick is to NEVER really go above a 15% credit utilization ratio, and to never overleverage. Tricky because very quickly you will get enough credit to go bankrupt)
Month 6: get credit report showing low balances, a slight dip in score from last quarter, but still high