The magnetic phases of the heavy rare-earth metal thulium below the Neel temperature of 56 K have been examined in magnetic fields up to 7 T. The thermal expansion and magnetostriction of a Tm single crystal were studied along the c-axis, using a capacitance dilatometer. A number of new magnetic phases appear in non-zero magnetic fields. These are intermediate phases between the c-axis modulated and 4 up, 3 down ferrimagnetic phases previously established.