If you modify something then you make a new product, unless it does exactly the same thing. but, remember, for example, that some products require type testing to meet the standard, if you modify such as to breach the type test, then that would be significant.
It's nothing to do with sticking with one manufacturer, unless you are talking about compliance with the EN 61439 series, or other equipment which is type tested.
You don't "need" a tool to CE mark, it can be done long hand. There is a LOT more to machinery controls, and designing and building electrical panels than is involved in BS 7671, and if you think that is expensive, then think again, most of the standards that need to be complied with to take a presumption of conformity cost 4 - 5 times what BS 7671 does.
If you go and fix a machine, and you take out a Siemens relay from a safety circuit, and fit a Schneider one, because that is your van stock, then you have invalidated the CE mark on the equipment and absolved the manufacturer of any liability. You then become liable as the manufacturer should your modification result in loss, injury or death. The same would apply to an e-stop button, or a safety door switch, door interlock etc.
It's a minefield, because you are straying into product law, and product liability, how many of you carry product liability insurance for products you manufacture?
