Hi pfluger,
You have several options depending on the amount of softening you want and of course your budget range.
The three general “levels” of “fine tuning” you would be choosing from are …
Mattress protectors: Generally for protection only and if anything designed to have the least possible effect on the mattress rather than changing it’s performance. There are a series of tradeoffs involved in these depending on the combination of waterproofing or water resistance, effect on the mattress (from a little to moderate in terms of increasing firmness) and breathability and temperature regulation. There’s more about the different types of mattress protectors here but because you may be looking to soften your mattress … this probably isn’t what you are looking for.
Mattress pads: These are generally in between the thickness of a mattress protector and a topper and to different degrees can sometimes combine the function of both (if the mattress pad is either water resistant or waterproof). This is probably closer to the “level” of fine tuning you are looking for.
Toppers: These come in a huge range of materials and thicknesses and are designed to make more significant changes to a mattress. A topper can add additional “comfort” and pressure relief to a mattress that is too firm and it can also help extend the useful life of a mattress underneath it. They range from about an inch all the way up to much thicker. If you go in this direction and choose a foam material you will need a cover to protect it (if it doesn’t already have one) in addition to the mattress protector that will go over it and the mattress for protection. There is more about toppers in post #2 here.
Since you are looking to combine both protection and potentially some extra surface softness … I would be looking at mattress pads. There are a huge amount of options but unfortunately finding good information about them is as difficult as other mattress materials so I’ll talk about them generically and add a few links to some resources. Like with mattresses … it’s often best to talk with a retailer that carries many different types and is familiar with the different types of feel and performance of their products to get a sense of which may be best rather than going by specs which are often incomplete.
Fiberbeds: These are generally made from polyester fibers with different types of fabric covers but you will also see these with other types of higher quality fibers that are also better at absorbing moisture such as viscose or that are plant sourced such as ingeo. They come in many different quality levels, thickness levels, and density of fill. They are a good choice for those who are looking at a lower budget range and don’t mind that they are less resilient and durable than higher quality materials. They will sometimes come with a waterproof polyurethane or polyethylene material to make them waterproof but less breathable. They will provide more of a surface softness and help specific pressure points more than they will provide more general pressure relief.
Down Alternatives: These are generally a higher quality polyester fiber that is finer and more “slippery” and are meant to simulate the feel of down. They are similar to the fiberbeds but have a more luxurious feel without the allergy or maintenance issues of down. They are also fairly resilient and can make a good “value” choice.
Down and feathers: Down is a great material for comforters or duvets but not as good for pads or toppers IMO. While they have a great and “plush” feel, they also compress very easily and require more maintenance and fluffing. They can also present allergy issues, are prone to dust mites, are not great with moisture, and in good quality (with good fill weights and down instead of feathers) can be very expensive. Different combinations of down and feathers are widely available which will affect resilience, comfort, breathability and warmth. They will also tend to be warmer than other materials. Of course there are also some people where nothing but a feather/down featherbed will do and personal preferences always “trumps” anything else in the end. A featherbed protector is a good idea if you go in this direction.
Wool: This is a more “premium” and versatile material and has a great combination of softness, breathability and temperature regulation, and water resistance. There is a wide range of products with different densities and thicknesses and they also are more expensive than lower quality materials. Wool is also more resilient so will compress less over time and maintain it’s loft better than other fibers depending on how it’s made and quilted. Wool is also very durable. They tend to come in two types which are fleece and batting with the fleece being more “loose” and without any cover over it and a backing of either cotton or polyester (which can make them washable) which will give it a softer initial feel but it will also compress more easily. The batting needs less “fluffing” or maintenance and is more resilient so the pressure relief and softness it provides is more widespread and less 'localized" than fleece although still not to the same degree as foam.
Silk: This is also a premium fiber which is very resilient, temperature regulating and durable. It is generally more expensive than wool and has similar benefits with the exception of water resistance so the possibility of “accidents” can play a role in choosing one of these. It’s a good option for those who like the idea and luxury of sleeping on silk and don’t mind paying the price for a more premium material (at least in good quality).
Cotton: Cotton tends to wick moisture well but will not absorb and hold it as much as wool without feeling damp. It is also less resilient and compresses more than wool so is not as suitable for “softening” a mattress, particularly over time, as more resilient fibers. It’s more suitable as a fabric around other materials especially in a stretch knit which has much less effect on the other materials. It is less “water resistant” that wool and is also more prone to dust mites than either wool or silk. It is very durable.
There are also some mattress toppers which use various types of foam (such as memory foam, polyfoam, or latex) which are in the range of an inch or so that would perform similar functions to a mattress pad. One of the differences though is that foam toppers are generally only for additional softness and not meant as much for protection against body oils and moisture and don’t have the same ability to wash or maintain as a mattress pad. They are typically used in combination with a protector. The advantages and disadvantages of a foam topper would be similar to the same materials used in the comfort layers of a mattress except that they would wear a little quicker (they can compress more independently) but can also be exchanged without buying a whole new mattress.
The outer fabric of a mattress pad is also important in terms of breathability with cotton or viscose (such as bamboo) being the better options than synthetic polyester fabrics which tend to be less breathable. There are also fabrics which use “phase change materials” such as outlast which will help regulate temperature by storing and releasing heat which can add to the temperature regulating properties of a mattress. An example is here.
More knowledgeable outlets like Allergy buyers Club (or their sister site Sleep Buyers Club) are often great resources because they personally test all of their products and have good comparative descriptions of the different materials on their site. Like with mattress materials … outlets like this which have good experiential knowledge can be invaluable and save a lot of frustrating research into various choices and never feeling like you are getting any closer to what a particular material will really feel like or how it will perform. The choices in materials can sometimes be overwhelming and finding accurate information about the quality ranges in each material can be very difficult.
http://www.cuddledown.com/category/mattress-pads-protectors.do They were also very informative and helpful on the phone and comfortable talking about materials and have a very good resource center about their different options and materials. They also have a good 30 day refund/exchange policy.
dreamsoftbedware.com They have a good selection of different products and materials but in my experience are not as knowledgeable on the phone about the differences between materials. They also don’t allow for returns or exchanges on bedding except for Snugfleece items.
Big box stores such as Walmart, Costco, Sams Club etc or online shopping portals such as Amazon (if they fulfill it) can also be good options if you are unsure because of their refund policies so you can test a product and return it if it doesn’t work the way you want it to. Most bedding products are not returnable in many outlets because they are considered “personal items”. Outlets such as Amazon can also be good resources if you know what you want and are looking for better value but the return policy will vary depending on who is fulfilling the order.
Hopefully this will give you some ideas and resources about what may work best for you once you and your mattress have gone through any initial “adjustment” period 
Phoenix
I didn’t know it existed.