A sms message has a hard upper limit of 160 characters, however it is possible to combine several sms messages into a "virtual" message that then appears to be longer. The technical name for this is multi-part, e.g. combining several sms messages into one virtual larger message.
Sending sms messages with AT commands can be done in two ways, text mode and pdu mode and notice that text mode only supports sending single sms messages; in order to send a multi-part message you must use pdu mode.
And to preempt any poor AT command handling, remember that you must wait for the ready to receive data prompt before sending the sms payload, and in general read and parse response lines from the modem waiting for the final result code.