@Anonymous wrote:First I would start with Chase prequalification site since they have their 5/24 rule. Once you have applied for chase then hit up American Express. At this point I would stop after two new cards but if you are frisky go ahead and apply for a citi card. I will say that if you are planning on buying a house in the next two years DONT go with this plan. Here is the deal: yes your credit score will take a hit for a short time because of this but you should be able to raise your total credit limit which affects utilization %. The good news is then you can go into the garden and stop applying for credit and let the new accounts all age together. This is not the best way to go if you like Start Up Bonuses since it might be difficult to get that much spend through and still pay the cards off but if increasing your total credit available or limit is the goal then go on a mini spree.
OP said they JUST bought a house and want new cards to cover remodeling. I would assume this would mean hitting Sign Up Bonuses wouldn't be hard at all.
OP, definitely diversify. Capital One isn't the end all, be all. Especially when it comes to limits. They can be hard to grow. 
@Anonymous wrote:Thanks everyone, sounds like the issue is cap1, and even with lots of use they don't grow.
Not exactly but that is true in-part. In general, the generosity of limits varies by lender. Capital One is known for issuing some cards which are "bucketed" (with lower limits) that refuse to grow, as well as for requiring a lot of spending to get modest increases on non-bucketed cards. There are exceptions. Some on the forums have Capital One cards well into five-figures and even into six-figure credit limits, but they are the exception. I had a $1K Platinum card that I very slowly grew over about a decade to a $25K Quicksilver card, so it can happen with patience. But yes, Capital One is a big part of your problem.
Gaining lender diversity and 'leveraging' higher limits over time is your best strategy, as others mentioned above. As your highest and average limits grow, your other cards generally follow.
Temper your expectations based on not only your credit score but also your income and debt-to-income parameters. Credit scores help drive approvals but those other variables are huge in credit limit considerations. Unless you have sizable invested assets or a high level of reimbursed business spending, most lenders award limits based on a combination of the existing limits you've shown you need and can handle, combined with your ability to repay (income and debts.) When household income rises and debt falls, those can both help leverage limits higher.
Using your cards regularly and responsibly, asking for CL increases as allowed, and patience are your best strategies.
