Some of the modifications require welding, machining, fitting, design, experience, and research.
The most common turbo modification I do, is a basic high flow. This is where the stock compressor wheel gets replaced with a larger one that flows better. Today the Billet compressor wheel are used because supply companies can now supply multiple versions of a chosen size. The size of the compressor is determined by the desired flow that is required. If a certain flow is beyond a level where a too large compressor wheel is needed, then the Turbine wheel needs To be upgraded so to drive such a large diameter compressor wheel. Increasing this rotating mass and size has a pay off and that is slower boost responce. You can't keep going bigger and bigger and expect nothing to change.
Beyond this opens up a whole range of upgrades possible depending on the turbo type. This includes mods to wastegate, bearings, oil supply, housings, ect.
The modifications to the stock frame turbo can be endless until the physical size of the housings restricts flow. As an example, the 2JZGTE JDM ct20 twin turbochargers have been modified to an extent where they can flow over 700rwhp.
Or the CT26 from the Supra 7mgte can flow 600hp from the single turbo extremely modified. This is the upper limit of flow from the compressor housing. Changing it to the much larger GT35 .7 AR compressor housing can increase that flow to over 700rwhp. Obviously, the rotor wheels need to be increased in size to match, as well as the bearings and wastegate. This sort of upgrade can raise the question on why not just change the whole turbo that is ment to do that. This is an option but would mean change, manifold, dump pipe, oil feed lines, oil drain, water cooling lines ect. A lot of expense and work for no gain.The majority of work I do are to the CT26. This is not by choice, it is what customer request from my business. I believe it is because the limited alternate bolt on upgrades available of decent quality, flow or reliability and development.
The most extreme version of modifications to the ct26 turbo I do, is the GT35 .7AR compressor adaption, 67mm billet compressor 9 blade 59mm turbine, tripple ball bearing(only one world wide) 40mm internal wastegate, ported turbine housing to increase AR size.
Modifications to increase flow are pointless if the gas flow to, or from the turbo is inadequate. The vehicle or engine manufacturers are only concerned how it flows or runs to suit the specified and designed engine output. Generally there is an allowable percentage of flow increase of about 20-30%, or less. Over this the restrictions can cause inefficiencies that can effect reliability and other issues. Manufactures don't care anything above stock HP. The aftermarket industry is flooded with upgrade components that can increase flow and these are just as important or more important as a modified turbo.
Generally what can be done, or how far a turbo can be modified, relies on the person, team or coordinator doing the mods. They need the proper research and experience through testing, data, information on the vehicle planned use and what is possible or available. This is the R&D required to do the job successfully. R&D(research and development) takes time and costs money. For a proper turbo upgrade the cost is not cheap if it is extensive. There are mass produced upgrade items available which helps a lot but they are mostly Chinese cheap versions. Take them at your own risk.
Carefully thought should be taken on what level upgrade mods are to get done. Not just "do an upgrade to my turbo". What upgrades,? how far? What hp? What boost? Purpose of vehicle. Having all this sorted out save time and will have less chance of misinformation or misleading. Going onto social media to get the information can be a dangerous and confusing rabit hole that will lead to confusing and conflicting results. It is best to speak to professionals experienced in the area. And ask them specific questions about details of the mods and why. If they cannot answer the specific question,(such as what parts are used and why) and just deliver "trust me", stay away! They need to know their shit.
Turbocharger mods always falls in line with a tuner. The turbo upgrade can change the characteristics of the engine and therefore the tune. Also the tuner can help with the extra lag or tell if the engine or tune is correct. The tuner is the final stage of an upgrade and the turbo is a big part of the upgrade. So the combination of tuner/turbo modifier is important.