Can I Keep Both Sabbath and Sunday?

No, you can't.

The Sabbath/Sunday issue is a matter of "who you worship", and God wants you to make a choice.

No man can serve two masters: for either he will hate the one, and love the other; or else he will hold to the one, and despise the other. Ye cannot serve God and mammon.
- Matthew 6:24 (KJV)

It's either the Sabbath (God's Commandments), or the Sunday (the commandments of men).

Remember that God is a jealous God.

Thou shalt have no other gods before me. Thou shalt not make unto thee any graven image, or any likeness of any thing that is in heaven above, or that is in the earth beneath, or that is in the water under the earth. Thou shalt not bow down thyself to them, nor serve them: for I the Lord thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me; And shewing mercy unto thousands of them that love me, and keep my commandments.
- Exodus 20:4-5 (KJV)

Every letter of the law must be kept.

For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled.
- Matthew 5:18 (KJV)

Church is on the Sabbath.

Six days shall work be done: but the seventh day is the sabbath of rest, an holy convocation; ye shall do no work therein: it is the sabbath of the Lord in all your dwellings.
- Leviticus 23:3 (KJV)

Sabbath is God's day, Sunday is satan's day.

It's just that simple.