Yes. With the Messages resource URI, you can send and receive messages containing up to 1,600 characters in standard GSM encoding, or up to 670 if Unicode characters are used.
For extensive details on how GSM vs. Unicode encoding works, and how this relates to concatenated messages, see: What the Heck is a Segment?
Sending outbound concatenated SMS
Concatenated messages are supported when sending to all major US/Canada carriers except for Sprint. Sprint does not support concatenated SMS. In addition, many smaller US/Canada carriers also support concatenated messages.
Twilio will auto-segment long SMS messages with a special header, which mobile carriers can use to reassemble the segments on the destination handset. Thus, concatenated SMS can appear as one single message on the receiving device.
You may also send messages over 160 characters to international phone numbers. However, they may appear as multiple messages on the destination handset, depending on whether the receiving carrier supports concatenated SMS.
Refer to our FAQ for how pricing works for outbound concatenated messages.
See also: What the Heck is a Segment? for extensive detail on SMS segmentation.
Receiving inbound concatenated SMS
Similarly, Twilio supports inbound concatenated messages up to 1,600 characters. Inbound messages over 160 characters will also be received on your Twilio phone number as one single message. The price of the inbound message will be the sum of the total number of segments.