Made with Blender 3.4
Change Mixamo Character in Blender

For this demo I will be using X-Bot from Mixmamo

Download the XBot and select 24 frames per second, leaving the rest default

Import the FBX in blender (File->Import->FBX)

Now we are going to make changes to this model.

Select in Object Mode the head
Blender selects the mesh Beta_surface

Go into Sculpt mode:

To add more geometry = points to sculpt around you can use the Multires modifier

Make sure that you still have the 'Beta_surface'selected.
Go into object mode again if you haven't. In Object Mode you can select another mesh to sculpt.

Go to the wrench icon and click on Add Modifier

And select Multiresolution

Click subdivide twice inside the multires properties

The division is done 2 for viewport, sculpt and render.

To see how many geometry you have to work with select the wireframe icon at the top

The viewport looks like this:

Click the solid icon to view the model in regular mode

Note: Do not use the dynotopo mechanism to create more geometry. This method will break the Bone Weights on the model and you will lose animations that are on the model

Make changes to the model by using the Grab tool.

I have made a nose by dragging a part of the face.

You can select the X-Mirror on top of the sculpt editor:

You will see mirrored yellow points (in the Grab tool) to indicate that you will be changing the geometry on both sides

These modifications will be sufficient for this time.

You can change materials on the model as well.
Click on the Beta Surface arrow to collapse the properties

Click on 'Use Nodes'

And select anoterh color

But in our case we are going to use vertex paint. So we will delete the color

Make sure you have the 'Beta_HighLimbsG' selected and Select X Delete from the Right Click Menu:

Vertex Painting
Select Vertex Paint from the left hand menu:

Choose a color from the color menu by clicking on the (default) white color

Default mode is Mix mode. This mode will combine the color on the mesh with the selected color
In this case there is no color on the mesh so it will be no problem, but I will point out that you can use both Color and Value selections from this menu to overwite color once you have a vertex paint

Now you can draw something

Export to FBX to be uploaded into Blender again
File->Export->FBX

Do not export Camera and Lamp object types, but (shift)select the others.

[Upload Character] and drag/select the created FBX file to Mixamo

The imported FBX file will have bone structure because we downloaded the model from Mixamo. You could be presented with a part of the import mechanism that will require you to place the chin,wrists,elbows,knees,groin rigging-points

But we have the option to use the Auto-Rigger and select [next]

Search for Standard walk [ top left of the screen ]

It should look something like this:

It could be that you made other changes to your model.
I will demostrate some behavior with a lot of scribbles
And where the Beta surface and joint meshes are combined

Vertex Paint Result

And imported in Blender with the Standard Walk animation

It does not at all look like the Blender Vertex Paint.

Do not worry. Download the standard walk from Mixamo

File->Import->FBX

It still does not look like it:

Go to the Shading view port:

Select the model

Add -> Search

Search for 'Color Attribute' and Add it :

Drag the Color dot to the Base Color on the Principled BSDF

Now the vertex paint shows up.

We can play the animation in the Layout Viewport

Switching Mixamo Animations