6-10 years might be a bit lofty, as technology progresses, 4-5 years seems to be a good shelf life for a system. As operating systems change, and the associated drivers and platforms that support even simple web browsing change (Java, Flash, Adobe Reader are some examples) there eventually becomes a need to update RAM, and even a video processor. If you are using the integrated graphics on a cpu and board, those will eventually need replacing. Using a separate gpu can add further life, at an increased cost.
What kind of multitasking? That involves a decent amount of high quality RAM. The current edge on mobo seated RAM modules is DDR4. High end gpu's have DDR5
Assuming no need for a case, power supply, monitor, OS, optical drive, or storage drive (although if you do not have an SSD that is something to invest in) the key components that impact performance are the CPU/motherboard RAM and video card.
So beyond multitasking...is this simply multiple windows/apps running simultaneously? Multiple monitors? What is the budget for an upgrade?