When increasing stitches when knitting in fisherman's rib, this is the method I like best.
The increases are made on a right side row, where the knit stitches are worked in the usual way, and all the purl stitches are slipped, with the yarn at the front of the work.
When increasing at the beginning of a row, to keep the edges neat, the first stitch is slipped, the second stitch is a knit stitch, and then the increase is made. The yarn that stretches between the second and third stitches is picked up...
… and in this picture can be seen on the right hand needle...
… then the left hand needle is passed through the front of the picked up stitch, and it is worked as a knit stitch through the back of the stitch.
Here you can see the increased stitch on the right hand needle.
Now the yarn is brought forward and the next stitch is slipped purlwise to continue the rest of the row.
To increase at the end of the row, when three stitches remain, bring the yarn forward and slip the purl stitch.
Next, the yarn between the stitches is picked up, and the increase made in the same way as shown at the beginning of the row.
Then the last two stitches are both knitted.
With the extra stitch at each end of the row, this means that there are two knit stitches side by side on a right side row, and two purl stiches on a wrong side row, until the next increase needs to be made.
The next time it is straightforward. The yarn between the two knit stitches is picked up in exactly the same way as shown above, and knitted through the back of the stitch.
On the next row the new stitch means that fisherman's rib can be worked as normal.