It is very common to do over here, both with a dry floating indicator or the likes of a Mayfly bomb to get deep. Both methods you tie the smaller/lighter pattern off the bend of the front fly with a short section of tippet of as little as 6" and up to say 24".
Why? Because it gets a small fly deep in the water column fast and doubles your chances. If you are going to add a weight it may as well have a hook in it, same with an indicator. You will be surprised just how often a trout will rise to a yarn indicator- even if there is no surface insect activity. Heck I know guys that fish here from the States and add hooks to yarn indicators while fishing here.
The two nymph or nymph soft hackle rig can also be a visual aid. The larger nymph can stimulate the chase and draw attention to the smaller nymph trailing behind.
If your Pink Squirrel is working at the correct depth and is weighted, try tying one of your small spider patterns off the back by tying it to the bend of the Pink Squirrel. I fished this a lot for wild Brown Trout in Northern Ireland, the locals all gasped a bit- but were very quiet when I started out fishing their single gold beadhead Pheasant tails.
Some waters have regulation regarding more than one fly at a time, some even have rules regarding adding weight, so check the regulations before you go changing too much and stay within the law.
To me, using some form of weight up the leader a bit, be it tungsten putty- another fly or split shot, lets the trailing fly align in the water more naturally than a beadheaded single, mostly because I believe most nymphs rise headfirst whilst hatching and this is when trout like to eat them. True there are unfortunate nymphs that get dislodged and tumble along the bottom willy-nilly in all kinds of shapes and positions, but if you allow a fly to swing and lift, I believe it behaves more like a natural if the fly itself is unweighted.
However
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You can experiment with the bead placement and tie it into the thorax area more than the head- thus giving a more even keel. You can even bury a small bead in the thorax and over wrap it with dubbing adding the weight, but not the visual illusion. Try some with the hackle behind the bead and tie some with the hackle in front. Hackle in front will help the hackle sit out from the body of the fly and not was back to cloak the abdomen if fishing across and down in reasonably fast water.
Different bead material will give you different visual effects and different weigh/sink rates. Plain brass, tungsten, plastic and glass beads all work. Play around and have some fun. The results will not be traditional spiders of the old world texts..... but I am guessing if the fish don't mind you will not either.
Now if you are not sick of reading yet...... toss all the above out the window and use a sink tip/sinking line or a sinking leader section.
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Some fishers use fullers earth to sink flies, or rub silt on the fly and leader. You can also get fly preparations that are deigned to sink your fly, same as the others designed to float it.
There are lots of ways to get your regular spider down to where the fish are. Part of the wonderful world of fly fishing is to discover all these things, take note of and use the ones you find useful and have a heck of a lot of fun doing it!