Make colour separations of your artwork as explained in the last edition of Stuck Illustrator Rescue Tips on Composition. It helps changing the separated colours to black for the next few steps. Save your separated colours in a flattened, black-on-white layer (or use multiple artboards with the separated colours and export them as flat PNG's in Adobe Illustrator). This is a great opportunity to play around with colour overlap as well: In my original artwork I am using five colours: blue, yellow, orange, green and black. I am including some colours in two separations: green shapes appear on both the blue and yellow separations, the black shapes appear on all three separations, which means the black colour will be made by multiplying the yellow, orange and blue colours from my original artwork. Reducing the number of separations makes for an easier work process, and the final colours look real nice too!
Start a new document in Photoshop with your separated colour layers, in my case three layers (A) Give each layer a bit of gaussian blur. The amount depends on the size of your artwork, play around with the blur settings if the end result isn't to your liking. For this 33x48cm poster artwork, I am using a 5px blur. (B) Now pump up the levels of your blurred layer to expand the shapes and adding a nice rounded edge to it. Make sure you slide up the shadows rather than bring down the highlights, as you want your shapes to expand rather than contract. (C) Repeat this step for all your separate colour layers. Now bring back your original colours. I do this by adding a new layer on top, filling it with the original colour and setting this layer opacity mode to 'screen'. Flatten these two layers and repeat for each colour, then set all layers opacity mode to 'multiply' - That should do the trick! Hope you like to try adding a bit of trapping to your artwork. Let me know if you have another quick way to do this or if you have any questions!