Use either circular or double-pointed needles to avoid having to cut threads.

To begin, loosely cast on (long tail over 2 needles) an even number of sts with
color A. Do not turn work.
My colors: color A = beige, color B = blue

Prep Row color B: slide work to other tip of needle, attach color B, *yf sl1yo,
k1; rep from *. Turn.
Row 1 color A: *yf sl1yo, brk1; rep from *. Do not turn work.
Row 2 color B: slide work to other tip of needle, *brp1, sl1yof; rep from *. Turn.
Row 3 color A: brk1, yf sl1yo; rep from *. Do not turn work.
Row 4 color B: slide work to other tip of needle, *sl1yof, brp1; rep from *. Turn.
Rep Rows 1-4.

For this sample I followed the instructions of the moss brioche stitch but
alternated colors A, B and C. Your yarns will be hanging on the correct side of
the work so you will not have to do any sliding.
My colors: color A = beige, color B = blue, color C = yellow green

To begin, loosely cast on (long tail over 2 needles) an even number of sts in
color A.
Prep Row: attach color B, *yf sl1yo, k1; rep from *. Now attach color C.
Rows 1 and 2: *yf sl1yo, brk1; rep from *.
Rows 3 and 4: *wyif, sl1yof, brp1; rep from *.
Repeat Rows 1-4 working one row in color A, then one row in color B and then
one row in color C, one row in color A, one row in color B, etc.