If it's a SOFT inquiry, that's okay. I think if your lower limit lenders see that you have that $2k limit on your report, they would be willing to do CLIs... Of course, ymmv with each individual lender
Marriott PR$25k | BCE $24.5K |BankAmericard Visa $25k| BOA Better Bal $17.5k |Wmt Discover $12.5k | BR Visa $17.5k | Amex Delta Gold $10k | Discover IT $10k | Paypal Extras MC $15k | Amazon Store $10k|Smile Gen $7.25k | Dillard's $10k | West Elm $4k| Express $3.05K | Mypoints.com Visa $4.5k | Freedom Visa $1k| Amex Surpass $1k