Putting in a dedicated power line. 2 receptacles ok?

Two is not an issue, on the same rail in the main box is. You have 2 120 vac rails. Use only one of the rails in the main.

As for the outlets you can have as many as you want, but remember the length of the wire/cable.  The further the run the higher the likely hood of an antenna affect, RFI EFI.

If you use the other leg (RAIL) you can create a ground loop. Do you understand? The difference in voltage between the TWO rails L1, L2 is usually where the noise happens. SLIGHT voltage difference, thus ground loop noise.  Because different gear is on different rails, (L1 and L2) in the main and common cabling between gear, we can create NOISE. 

I won't put up with it.. mine is dead quiet because of that alone.
Using only one side of the HOUSE MAIN... Keep the grounds and common separate in the main too.. Whole different story..  I've seen a lot of mixing the two together. Things work BUT there is a lot of voltage leakage in the circuit because of it.. Mixing the two only increases noise potential. Sometimes it's very difficult to track that type of noise down..

Regards

I'm not following you. There are opposite legs in your breaker box for ground?
L1
L2
Common bus bar
(bridge bar (remove or leave) between common and ground)
Ground bus bar

Where is the second ground bus in a 220-240 single phase main?

+1 @oldhvymec .
We need an explanation.

Sorry, in your breaker box you have two sides or rows of breakers. By having them on opposite sides the ground is then not interacting with each other which reduces noise. I had a master electrician do the install and it was his recommendation, it made sense to me that each circuit is independent of the other. I realize that only 3 wires come into the house and there is only one ground, but somehow he felt it was best.

That's ok if it makes sense to you.. It still doesn't to me.. BUT who the heck am I.. I think I'll stick with what I've been doing.. I mean I did build the house. NOT somebody else I built it, wired it, and and now repairing it after 40 years.. BUT hay, I'm just al ol mechanic..

Being able to do, rough wiring, pole work, troubleshooting, or finish wiring is NOT a hard thing to do. BEING fast and making it look professional is Pure repetition and do the good ones pay. For that a decent electrician in new construction it's almost worth hiring just for the speed alone. Cool thing my brother was the BA for the IBEW local 302.  With a little research you can figure out who I am.. NO lack of UNION Electricians around here.. Electricians, Mechanics, Cops, and Killers, My family!!

Regards

Convenience and short runs to the outlets are important considerations. 

In the US, using the NEC as guidance, yes, you can run a 15 or 20 AMP circuit to multiple outlets. 

In the NEC there are also requirements for having enough outlets on a wall.  I forgot what they are, but in general the idea is to minimize the need for extension cords.  I strongly encourage you to follow this minimum guidance at least. 

Best,

E