Socket n RX Write Pointer Register Update

I suppose that I will get a INT when a complete TCP/IP frame was received.
But I have some latency from int to readout. After Int I clear the RECV int flag.

Then I start to read out the data from the socket ram.

Whats happened, if while readout the data and a next Frame will arrive during this time.
Will Socket n RX Write Pointer Register updated byte by byte or after a complete frame.

Will a new INT be issued?

You will se a simplifier circuit diagram to understand the Register for receive.
IS this assumption correct?