403(b) and IRA can I combine?

I contributed $3600 to my 403(b) this year and would like to make a larger contribution for retirement. I am over 50. Can I contribute more by other means? E.g., can I contribute to an IRA? I am aware that other contributions would not change my tax liability.

If yes, what are the limits? Can I still contribute $8000 to an IRA? Or can I only contribute $4400?

 

Thanks in advance!