a few suggestions:
1. check for LE offers periodically. if there are no offers, try to email the bank requesting them to increase limit based on your spends (you will need to spend a good enough on that card in a planned manner - I did that and I was successful). do not try to do this with banks like bob, pnb, federal, etc etc (you get my point).
your best bet is axis, HDFC, ICICI, idfc as they are in the race for capturing credit card market and may heed your request. ASK AND THOU SHALT GET.
2. use this increased LE to go for C2C in other banks or an upgrade in current bank.
3. visit bank and meet an RM with your request. give them some business, they will give you what you want in return.
do the above 3 things during the last week of the month or financial year where banks are on a full swing to complete their sales targets.
some gyaan (for free):
4. don't go after premium cards just for flaunting 'status'. unless you are willing to bear the burden of fees and running after milestones in return for that status symbol. I personally run after savings and reward rate. premium cards know that people who can afford their premium fees do not care about reward rates and hence, these cards are (MOSTLY) designed for 'lifestyle' rather than rewards. an ltf ICICI platinum card gives you the same discount as an emeralde. an ltf axis also gives you the same lounge access where magnus holders sit. an ltf idfc card holder also sits adjacent to an au zenith holder in a movie theatre with bogo/50% discount offers.
5. it will take time. as you grow in age, income, expenditure, so will your card eligibility. a 21 year old with a 2 yr job experience wanting super premium cards equivalent to a 30yr old with 10yrs experience is unrealistic.
I have been through this journey (though only since the last 2 years). but you have to keep your eyes and ears open for marketing campaigns and also be aware that you don't fall to frauds. for eg the kotak white ltf thread.