You can do that with GROUNDS. Not Neutral!
Sharing grounds like that is OK, because ground never carries current except during fault conditions, which aren't supposed to last very long if the breaker is doing its job. So it's acceptable to assume 2 circuits won't have a problem at the same time.
Neutral carries the regular service current. Obviously putting ten 20A circuits for nominally 200A neutral current will not work on a #10 neutral. (let's just ignore MWBCs for now.)
However there are two better ways.
Way #1: Accessory ground bar(s)
Panel makers offer accessory ground bars to be field-installed to pre-planned sites in the panel enclosure. There are nubs and screw holes already drilled and tapped. The model numbers of "perfect fit" ground bar are listed on the panel labeling.
So, simply run out and buy the biggest of those ground bars that you please to get, and populate any or all such sites in the panel. Then you can move ground wires onto those accessory ground bars.
Why do they make you buy accessory ground bars? Why not free? Because the vast majority of panels sold either are main panels (allowing the next solution) or use metal conduit such as EMT, which does not require ground wires at all. I don't have any ground bars in my panels. They would be empty.
Way #2: Stuff the ground bars to the max.
To be clear, Code requires that each neutral wire be alone on its lug on the neutral bar.
Inside a main panel, grounds are allowed on the neutral bar. They can be doubled or tripled on each lug -- read the panel labeling (this again) and it will tell you exactly what is allowed.
If you have accessory ground bars, again the labeling will tell you if/how they can be doubled or tripled (this may be a different number than for the neutral bar).
UL requires the manufacturer to specify how many circuits are allowed on the panel. And then enough neutral lugs for every neutral and ground assuming the grounds are doubled/tripled as much as is allowed. Thus, a 20-space/30-circuit panel must have at least 40 neutral slots. 30 for neutral and 10 for grounds triple-stacked.
Most people struggling with neutral/ground spaces are unaware of the ability to stack grounds.
Is there any such thing as an accessory neutral bar?
Probably not. The reason is: Neutral bars must be rated/tested/certified to carry full normal service current rating, and that means "thermally". Grounds don't have that thermal problem since their current is transient. But ask your manufacturer. Or Eaton if your manufacturer is Cutler-Hammer [a brand of Eaton] or BRyant (bought by Cutler-Hammer).
The usual place people get in trouble with full neutral bars is when they have e.g. a 20-space/20-circuit panel and they're "illegally" using non-CTL tandems to cram more than that many circuits in there. The builder only gave them 27 neutral spots in that case. (20 for neutrals 7 for triple-stacked grounds). I say "illegally" because the CTL rule is gone. The labeling still binds - UL only certified a particular panel for e.g. 20 circuits. However UL has the right to change that retroactively if the manufacturer can convince them. One of UL's questions is "where do the extra neutrals go?" and the manufacturers' answer might be "Ta daaa! Accessory neutral bar."