How do I combine more ingredients during Alchemy?

You can only use three different ingredients per potion. However, each ingredient has 4 potential effects. Any effect which is shared by at least 2 of the ingredients will exist on the potion. So you can end up with a number of effects if you have ingredients that share a lot, but you cannot exceed three ingredients.

6 effects is theoretically possible, but after running a java script to combine all possible sets of 3 ingredients, i found that there is no potion with 6 effects.

There are, however, 5 potions with 5 effects.

EDIT: Since you ask, Holger, here they are :) Theese are the 5 combinations, listed with value first (calculated by values from this site: http://www.uesp.net/wiki/Skyrim:Alchemy_Effects )

636 Glowing Mushroom, Hanging Moss, Glow Dust.

555 Creep Cluster, Scaly Pholiota, Mora Tapinella.

542 Eye of Sabre Cat, Hanging Moss, Bear Claws.

470 Blisterwort, Jarrin Root, Human Heart.

263 Daedra Heart, Eye of Sabre Cat, Silverside Perch.

As you can see, not all of them are great value in spite of having 5 effects. The first one is still the most valueable potion you can create, even considering the huge boost you get from creating a Fortify Health potion using Giant's toe.

The second most valuable potion is this one (which only has 3 effects):

614 Giant's Toe, River Betty, Large Antlers.